MCQ 1011 Mark
Tick $(\checkmark)$ the correct answer the following:
$0.0000463$ in standard form is:
- A
$463\times10^{-7}$
- ✓
$4.63\times10^{-5}$
- C
$4.63\times10^{-9}$
- D
$46.3\times10^{-6}$
AnswerCorrect option: B. $4.63\times10^{-5}$
B. $4.63\times10^{-5}$
Solution:
$0.0000463$
$=\frac{463}{10000000}$
$=\frac{463}{10^2\times10^5}$
$=\frac{4.63}{10^5}$
$=4.63\times10^{-5}$
View full question & answer→MCQ 1021 Mark
$0.07 \times 10^{10}$ is equal to:
- ✓
$700000000$
- B
$7000000$
- C
$7000$
- D
$7$
AnswerCorrect option: A. $700000000$
A. $700000000$
Solution:
$0.07 \times 10^{10} = 700,000,000.$
View full question & answer→MCQ 1031 Mark
$\frac{5^4}{5^2}$ is equal to:
- A
$5^6$
- ✓
$5^2$
- C
$5^{-6}$
- D
$5^{-2}$
AnswerB. $5^{2}$
Solution:
By exponent law:
$\frac{\text{a}^\text{m}}{\text{a}^\text{n}} = \text{a}^{\text{m}-\text{n}}$
$\frac{5^4}{5^2} = 5^{4-2} = 5^2$
View full question & answer→MCQ 1041 Mark
$700000000$ is equal to:
- ✓
$7 \times 10^8$
- B
$7 \times 10^7$
- C
$7 \times 10^6$
- D
$7 \times 10^9$
AnswerCorrect option: A. $7 \times 10^8$
A. $7 × 10^8$
View full question & answer→MCQ 1051 Mark
For any two non$-$zero rational numbers $a, \text{a}^7\div\text{a}^{12}$ is equal to:
- A
$\text{a}^5$
- B
$\text{a}^{-19}$
- ✓
$\text{a}^{-5}$
- D
$\text{a}^{19}$
AnswerCorrect option: C. $\text{a}^{-5}$
$\text{a}^\text{m}\div\text{a}^\text{n}=\text{a}^{\text{m}-\text{n}}$
Hence,
$\text{a}^\text{7}\div\text{b}^{12}$
$=\text{a}^{7-12}$
$=\text{a}^{-5}$
View full question & answer→MCQ 1061 Mark
$3^m+3^{-3}=3^5 \Rightarrow m$ is equal to:
AnswerB. $2$
Solution:
$3^m+3^{-3}=3^5$
$\Rightarrow 3^{m+3}=3^5 $
$\Rightarrow m+3=5 $
$\Rightarrow m=2$
View full question & answer→MCQ 1071 Mark
What is the usual form of $7.54 \times 10^{-3}?$
- A
$0.0754$
- ✓
$0.00754$
- C
$0.000754$
- D
$0.0000754$
AnswerCorrect option: B. $0.00754$
B. $0.00754$
View full question & answer→MCQ 1081 Mark
$3^2 \times 3^{-4} \times 3^5$ is equal to:
AnswerC. $3^3$
Solution:
$3^{2} × 3^{-4} × 3^{5} = 3^{2-4+5} = 3^3$
View full question & answer→MCQ 1091 Mark
The value of $\text{log}24\ – \text{log}15 + \text{log}40 $ is equal to:
- ✓
$5\text{log}2$
- B
$7\text{log}2$
- C
$6\text{log}2$
- D
$8\text{log}2$
AnswerCorrect option: A. $5\text{log}2$
$5\text{log}2$
View full question & answer→MCQ 1101 Mark
Square of $\Big(\frac{-2}{3}\Big)$ is:
- A
$-\frac{2}{3}$
- B
$\frac{2}{3}$
- C
$-\frac{4}{9}$
- ✓
$\frac{4}{9}$
AnswerCorrect option: D. $\frac{4}{9}$
To square a number is to raise it to the power of $2.$
Hence, thesquare of $\Big(\frac{-2}{3}\Big)$ is $\frac{(-2)^2}{3^2}=\frac{4}{9}$
View full question & answer→MCQ 1111 Mark
$3^{2} \times 4^{2}$ is equal to:
AnswerC. $144$
Solution:
By exponent law;
$a^m × b^m = (ab)^m$
$3^2 \times 4^2 = (3 \times 4)^2 = 12^2 = 144$
View full question & answer→MCQ 1121 Mark
The multiplicative inverse of $10^{-100}$ is:
- A
$10$
- B
$100$
- ✓
$10^{100}$
- D
$10^{-100}$
AnswerCorrect option: C. $10^{100}$
C. $10^{100}$
Solution:
For multiplicative inverse, let a be the multiplicative inverse of $10^{-100}.$
so, $a \times b = 1$
$\therefore$ $a \times 10^{100} = 1$
$\Rightarrow\text{a}=\frac{1}{10^{-100}}\times\frac{1}{\frac{1}{10^{100}}}\ \Big[\because\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}}\Big]$
$=10^{100}$
View full question & answer→MCQ 1131 Mark
$503600$ is equal to:
- ✓
$5.036 \times 10^5$
- B
$5.036 \times 10^6$
- C
$5.036 \times 10^4$
- D
$5.036 \times 10^7$
AnswerCorrect option: A. $5.036 \times 10^5$
A. $5.036 \times 10^5$
Solution:
$503600 = 5.036 \times 10^5$
View full question & answer→MCQ 1141 Mark
$\frac{\text{a}^\text{m}}{\text{b}^\text{m}}$ is equal to bm.
- ✓
$\big(\frac{\text{a}}{\text{b}}\big)^\text{m}$
- B
$\big(\frac{\text{b}}{\text{a}}\big)^\text{m}$
- C
$\big(\frac{\text{a}^\text{m}}{\text{b}}\big)^\text{m}$
- D
$\big(\frac{\text{a}}{\text{b}^\text{m}}\big)^\text{m}$
AnswerCorrect option: A. $\big(\frac{\text{a}}{\text{b}}\big)^\text{m}$
$\big(\frac{\text{a}}{\text{b}}\big)^\text{m}$
View full question & answer→MCQ 1151 Mark
$5^3 \times 5^{-1}$ is equal to:
- A
$5$
- B
$5^3$
- C
$5^{-1}$
- ✓
$5^2$
AnswerD. $5^2$
Solution:
$5^3 \times 5^{-1} = 5^{3-1} = 5^2$
View full question & answer→MCQ 1161 Mark
Tick $(\checkmark)$ the correct answer the following : $\Big(\frac{-5}{3}\Big)^{-1}=\ ?$
- A
$\frac{5}{3}$
- B
$\frac{3}{5}$
- ✓
$\frac{-3}{5}$
- D
AnswerCorrect option: C. $\frac{-3}{5}$
$\Big(\frac{-5}{3}\Big)^{-1}=\Big(\frac{-3}{5}\Big)^{1}$
$=\frac{-3}{5}\ \bigg\{\because\Big(\frac{1}{\text{x}}\Big)^{-\text{m}}=\text{x}^\text{m}\bigg\}$
View full question & answer→MCQ 1171 Mark
$\Big(\frac{2}{3}\Big)^{-5}$ is equal to:
AnswerCorrect option: B. $\Big(\frac{3}{2}\Big)^5$
Rearrange $\Big(\frac{2}{3}\Big)^{-5}$ to get a positive exponent.
$\Big(\frac{2}{3}\Big) ^{-5}=\frac{1}{\big(\frac{2}{3}\big)^5}$
$=\frac{1}{2^5}$
$=\frac{\frac{3^5}{2^5}}{3^5}$
$=\frac{3^5}{2^5}$
$=\Big (\frac{3}{2}\Big)^5$
View full question & answer→MCQ 1181 Mark
$(-1)^{51}$ is equal to:
AnswerA. $-1$
Solution:
$(-1)$ odd natural number $= -1$
View full question & answer→MCQ 1191 Mark
$1.8 \times 10^{11}$ is equal to:
- ✓
$180000000000$
- B
$18000000000$
- C
$1800000000$
- D
$1800000000000$
AnswerCorrect option: A. $180000000000$
A. $180000000000$
View full question & answer→MCQ 1201 Mark
If $x$ be any integer different from zero and $m$ be any positive integer, then $x^{-m}$ is equal to:
AnswerCorrect option: C. $\frac{1}{\text{x}^\text{m}}$
C. $\frac{1}{\text{x}^\text{m}}$
Solution:
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}}$ [$\because$ a is non-zero integer]
Similarly,
$\text{x}^{-\text{m}}=\frac{1}{\text{x}^\text{m}}$
View full question & answer→MCQ 1211 Mark
What is the reciprocal of $\Big(\frac{-3}{4}\Big)^\circ?$
- A
$-1$
- ✓
$1$
- C
$\frac{-4}{3}$
- D
$\frac{4}{3}$
AnswerReciprocal of $\Big(\frac{-3}{4}\Big)^\circ=\Big(\frac{4}{3}\Big)^\circ$
(as we know a to the power zero equals to $1)$
$=\Big(\frac{4}{3}\Big)^\circ=1$
View full question & answer→MCQ 1221 Mark
Which of the following is the standard form of $0.00001275?$
- ✓
$1.275 \times 10^{-5}$
- B
$12.75 \times 10^{-5}$
- C
$127.5 \times 10^{-7}$
- D
$127.5 \times 10^{-9}$
AnswerCorrect option: A. $1.275 \times 10^{-5}$
A decimal is a number which represents the tenths, hundredths, thousandths, and so on using the decimal points.
The standard form of decimals are used to represent the large numbers into the smallest using the multiplication of the number with $10$ to the power of places it is distanced from the decimal.
$\because0.00001275=\frac{1275}{100000000}$
$=\frac{1275}{10^8}=\frac{1.275\times10^3}{10^8}$
$\therefore1.275\times10^{3-8}=1.275\times10^{-5}$
$\because$ size of plant cell is $1.275\times10^{-5}\text{m}$
View full question & answer→MCQ 1231 Mark
Tick $(\checkmark)$ the correct answer the following : $\big(2^{-5}\div2^{−2}\big) = ?$
- A
$\frac{1}{128}$
- B
$\frac{-1}{128}$
- C
$-\frac{1}{8}$
- ✓
$\frac{1}{8}$
AnswerCorrect option: D. $\frac{1}{8}$
$\big(2^{-5}\div2^{-2}\big)$
$=2^{-5-(-2)}$
$=2^{-5+2}$
$=2^{-3}\{\because\text{a}^\text{m}\div\text{a}^\text{n}=\text{a}^{\text{m-n}}\}$
$=\frac{1}{2^3}$
$=\frac{1}{8}$
View full question & answer→MCQ 1241 Mark
Express $9^{-3}$ as a power with base $3.$
- A
$3^{-5}$
- B
$3^{-1}$
- C
$3^{6}$
- ✓
$3^{-6}$
AnswerCorrect option: D. $3^{-6}$
D. $3^{-6}$
Solution:
We know that $9 = 3 \times 3 = 3^2$
$(9)^{-3} = (3 \times 3)^{-3}$
$= (3^2)^{-3} (a^m)^n = a^{m \times n}$
$= 3^2 \times (-3)$
$=3^{-6}$
View full question & answer→MCQ 1251 Mark
$2.1 \times 10^{-6}$ is equal to:
- ✓
$0.0000021$
- B
$0.000021$
- C
$0.00021$
- D
$0.0021$
AnswerCorrect option: A. $0.0000021$
A. $0.0000021$
solution:
$2.1 \times 10^{-6} = 0.0000021$
View full question & answer→MCQ 1261 Mark
$10^{-1}$ is equal to:
- A
$10$
- B
$-1$
- ✓
$\frac{1}{10}$
- D
$-\frac{1}{10}$
AnswerCorrect option: C. $\frac{1}{10}$
C. $\frac{1}{10}$
Solution:
$10^{-1} = \frac{1}{10^1}=\frac{1}{10}$
View full question & answer→MCQ 1271 Mark
For any two non-zero rational numbers x and y, $x^4 \div y^4$ is equal to:
- A
$(x \div y)^0$
- B
$(x \div y)^1$
- ✓
$(x \div y)^4$
- D
$(x \div y)^8$
AnswerCorrect option: C. $(x \div y)^4$
C. $(x \div y)^8$
Solution:
Using law of exponents, $\frac{\text{a}^\text{m}}{\text{b}^\text{m}}=\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}$ [$\because$ a and b are non-zero integers]
Similarly,
$x^4 \div y^4$
$=\Big(\frac{\text{x}}{\text{y}}\Big)^4$
$=(\text{x}\div\text{y})^4$
View full question & answer→MCQ 1281 Mark
$\frac{5^7}{6^7}$ will give the value:
- ✓
$\big(\frac{5}{6}\big)^7$
- B
$\big(\frac{5}{6}\big)^0$
- C
$\big(\frac{5}{6}\big)^{-7}$
- D
$\big(\frac{6}{5}\big)^{-7}$
AnswerCorrect option: A. $\big(\frac{5}{6}\big)^7$
By exponent law:
$\frac{\text{a}^\text{m}}{\text{b}^\text{m}} = \big(\frac{\text{a}}{\text{b}}\big)^\text{m}$
$\frac{\text{5}^\text{7}}{\text{6}^\text{7}} = \big(\frac{\text{5}}{\text{6}}\big)^\text{7}$
View full question & answer→MCQ 1291 Mark
The multiplicative inverse of $\frac{1}{2^2}$ is $2^2.$
AnswerB. $2^2$
Solution:
$\frac{1}{2^2} = 2^2 =1$
View full question & answer→MCQ 1301 Mark
The value of $\text{log}^{80}_2+\text{log}^{5}_2-\text{log}^{20}_2-\text{log}^{10}_2$ is equal to:
View full question & answer→MCQ 1311 Mark
The value of $2^3$ is _____.
View full question & answer→MCQ 1321 Mark
Which of the following is not the reciprocal of $\Big(\frac{2}{3}\Big)^4$ ?
- A
$\Big(\frac{3}{2}\Big)^4$
- ✓
$\Big(\frac{3}{2}\Big)^{-4}$
- C
$\Big(\frac{2}{3}\Big)^{-4}$
- D
$\frac{3^4}{2^4}$
AnswerCorrect option: B. $\Big(\frac{3}{2}\Big)^{-4}$
Reciprocal of a is $\frac{1}{\text{a}}$.
Similarly,
$\Big(\frac{2}{3}\Big)^4$
$=\Big(\frac{3}{2}\Big)^4=\frac{3^4}{2^4}$
$=\Big(\frac{2}{3}\Big)^{-4}$
Hence,
option $(b)$ is not the reciprocal of $\Big(\frac{2}{3}\Big)^4$
View full question & answer→MCQ 1331 Mark
Find the multiplicative inverse of $5^{-3}.$
- ✓
$5^3$
- B
$\frac{1}{5}$
- C
$5^2$
- D
$5^{-2}$
AnswerA. $5^3$
Solution:
The multiplicative inverse of $5^{-3}$ is $5^3.$
$5^{-3} \times 5^3 = 1$
View full question & answer→MCQ 1341 Mark
The multiplicative inverse of $\Big(-\frac{5}{9}\Big)^{-99}$ is:
- ✓
$\Big(-\frac{5}{9}\Big)^{99}$
- B
$\Big(\frac{5}{9}\Big)^{99}$
- C
$\Big(\frac{9}{-5}\Big)^{99}$
- D
$\Big(\frac{9}{5}\Big)^{99}$
AnswerCorrect option: A. $\Big(-\frac{5}{9}\Big)^{99}$
For multiplicative inverse, a is called multiplicative inverse of b, if $a \times b = 1.$
Put b = $\Big(-\frac{5}{9}\Big)^{-99}$
$\Rightarrow\text{a}\times\Big(\frac{-5}{9}\Big)^{-99}=1$
$\Rightarrow\text{a}=\frac{1}{\frac{-5}{9}}^{-99}$
$\Rightarrow\text{a}=\Big(-\frac{5}{9}\Big)^{99}\ \Big[\because\text{a}^{-\text{m}}=\frac{1}{\text{a}^{\text{m}}}\Big]$
View full question & answer→MCQ 1351 Mark
Tick $(\checkmark)$ the correct answer the following:
If $(2^{3 x - 1} + 10) \div 7 = 6$ then $x$ is equal to:
AnswerD. $2$
Solution:
$\big[2^{3\text{x}-1}+10\big]\div7=6$
$=2^{3\text{x}-1}+10=6\times7$
$=2^{3\text{x}-1}+10=42 $
$\Rightarrow2^{3\text{x}-1}=42-10$
$\Rightarrow2^{3\text{x}-1}=32$
$\Rightarrow2^{3\text{x}-1}=(2)^5$
$\therefore3\text{x}-1=5$
$\Rightarrow3\text{x}=5+1$
$\Rightarrow3\text{x}=6$
$\Rightarrow\text{x}=\frac{6}{3}$
$\Rightarrow\text{x}=2$
View full question & answer→MCQ 1361 Mark
Simplify : $(-5)^5\times(15)^{-9}$
- ✓
$\frac{1}{(5)^4}$
- B
$\frac{1}{(5)^{-1}}$
- C
$(-5)^4$
- D
$(-5)^{-4}$
AnswerCorrect option: A. $\frac{1}{(5)^4}$
$(-5)^5\times(15)^{-9} = (-5)^{(5+(-9))}$ $(\text{a}^\text{m}\times\text{a}^\text{n}=\text{a}^{\text{m+n}})$
$= (-5)^{(5-9)}=(-5)^{-4}$
$=\frac{1}{(5)^4}$ $\Big(\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}}\Big)$
View full question & answer→MCQ 1371 Mark
Which of the following is not equal to $\Big(\frac{-3}{5}\Big)^4?$
AnswerCorrect option: C. $-\frac{3^4}{5^4}$
$\Big(\frac{-3}{5}\Big)^4$
$=\frac{(-3)^4}{5^4}$
$=\frac{3 ^4}{(-5)^4}$
$=\frac{-3}{5}\times\frac{-3}{5}\times\frac{-3}{5}\times\frac{-3}{5}$
It is not equal to $-\frac{3^4}{5^4}.$
View full question & answer→MCQ 1381 Mark
The multiplicative inverse of $\frac{2}{-3}$ is:
- A
$\frac{-2}{3}$
- B
$\frac{3}{2}$
- C
$\frac{1}{3}$
- ✓
$\frac{-3}{2}$
AnswerCorrect option: D. $\frac{-3}{2}$
The multiplicative inverse also known as reciprocal implies is something that is opposite.
The reciprocal number obtained in such a way that the value is equal to identity $1$ when multiplied by the original number.
Let us consider the number ‘a’ then the multiplicative inverse of the number is $\frac{1}{\text{a}}$.
$\text{a}\times\frac{1}{\text{a}}=1$
The given value is $\frac{-2}{3}, $ so
$\frac{-2}{3} \times\frac{-3}{2}$
$\Rightarrow 1$ The multiplicative inverse of $\frac{-2}{3}$ is $\frac{-3}{2}.$
View full question & answer→MCQ 1391 Mark
Mark $(\checkmark)$ against the correct answer of the following:
$(3^{-6} \div 3^4) = ?$
- A
$3^{-2}$
- B
$3^{2}$
- ✓
$3^{-10}$
- D
$3^{10}$
AnswerCorrect option: C. $3^{-10}$
C. $3^{-10}$
Solution:
$=\big(3^{-6}\div3^4\big)$
$=\Big(\frac{1}{3^{-6}}\div3^4\Big)$
$=\frac{1}{3^6}\times\frac{1}{3^4}$
$=\frac{1}{3^{(6+4)}}$
$=\frac{1}{3^{10}}$
$=3^{-10}$
View full question & answer→MCQ 1401 Mark
$1.5 \times 10^{11}$ is equal to:
- ✓
$150000000000$
- B
$15000000000$
- C
$1500000000$
- D
$500000000000$
AnswerCorrect option: A. $150000000000$
A. $150000000000$
Solution:
$1.5 \times 10^{11} = 150,000,000,000$
View full question & answer→MCQ 1411 Mark
The value of $(3^4)^3$ is:
AnswerCorrect option: B. $3^{12}$
B. $3^{12}$
Solution:
By law of exponent,
$(a^m)^n = a^{mn}$
$(3^4)^3 = 3^{4 \times 3} = 3^{12}$
View full question & answer→MCQ 1421 Mark
The value of $3^5 \div 3^{-6}$ is:
- A
$3^5$
- B
$3^{-6}$
- ✓
$3^{11}$
- D
$3^{-11}$
AnswerCorrect option: C. $3^{11}$
C. $3^{11}$
Solution:
Using law of exponents, $a^m + a^n = a^{m-n}$[$\because$ a is non-integer]
$3^{5} \div 3^{-6}$ = $3^{5-(-6)}$
= $3^{5+6}$
= $3^{11}$
View full question & answer→MCQ 1431 Mark
For a non-zero rational number $p, p^{13} \div p^8$ is equal to:
- ✓
$p^5$
- B
$p^{21}$
- C
$p^{-5}$
- D
$p^{-19}$
AnswerA. $p^{5}$
Solution:
Using law of exponents, $a^m \div a^n = (a)^{m-n}$ [$\because$ a is non-zero integer]
Similarly
$p^{13} \div p^8 = (p)^{13-8}$
=$p^{5}$
View full question & answer→MCQ 1441 Mark
$\Big(\frac{-3}{2}\Big)^{-1}$ is equal to:
- A
$\frac{2}{3}$
- ✓
$-\frac{2}{3}$
- C
$\frac{3}{2}$
- D
AnswerCorrect option: B. $-\frac{2}{3}$
We have:
$\Big(\frac{-3}{2}\Big)^{-1}=\frac{1}{\frac{(-3)}{2}}$
$=\frac{2}{-3}$
View full question & answer→MCQ 1451 Mark
In $10^2,$ the exponent is:
View full question & answer→MCQ 1461 Mark
Mark $(\checkmark)$ against the correct answer of the following : $\Big(\frac{3}{5}\Big)^{0}=\ ?$
- A
$\frac{5}{3}$
- B
$\frac{3}{5}$
- ✓
$1$
- D
$0$
AnswerUsing the law of exponents, which says $\Big(\frac{\text{a}}{\text{b}}\Big)^0=1$,
We get, $\Big(\frac{3}{5}\Big)^{0}$
View full question & answer→MCQ 1471 Mark
Write the expression using exponents: $89 \times 89 \times 89 \times 89.$
AnswerCorrect option: A. $89^4$
A. $89^4$
View full question & answer→MCQ 1481 Mark
$3^2 \times 4^2$ is equal to:
AnswerC. $144$
Solution:
By exponent law;
$a^m \times b^m = (ab)^m$
$3^2 \times 4^2 = (3 \times 4)^2 = 12^2 = 144$
View full question & answer→MCQ 1491 Mark
When we have to add numbers in standard form, we convert them into numbers with the $...........$ exponents.
View full question & answer→MCQ 1501 Mark
$a^\circ$ is equal to:
View full question & answer→