Question 12 Marks
Simplify:$\bigg[\Big(\frac{1}{3}\Big )^{-3}-\Big(\frac{1}{2}\Big)^{-3}\bigg]\div\Big(\frac{1}{4}\Big)^{-3}$
Answer$\bigg[\Big(\frac{1}{3}\Big )^{-3}-\Big(\frac{1}{2}\Big)^{-3}\bigg]\div\Big(\frac{1}{4}\Big)^{-3}$
$=[(3)^3-(2)^3]\div(4)^3$
View full question & answer→Question 22 Marks
Simplify:
$\Bigg[\bigg\{\Big (\frac{-1}{4}\Big)^2\bigg\}\Bigg ]^{-1}$
Answer$\Bigg[\bigg\{\Big (\frac{-1}{4}\Big)^2\bigg\}\Bigg ]^{-1}=\Big(\frac{-1}{4}\Big)^{2\times(-2)(-2)}$
$=\Big(\frac{-1}{4}\Big)^4=\Big(\frac{-1}{4}\Big)\times\Big(\frac{-1}{4}\Big)\times\Big (\frac{-1}{4}\Big)\\ \times\Big(\frac{-1}{4}\Big )=\frac{1}{256}$
View full question & answer→Question 32 Marks
Write the following numbers in the usual form:
$3.61492 \times 10^6$
Answer$3.61492 × 10 ^6$
$=3.61492\times1000000$
$=3614920$
View full question & answer→Question 42 Marks
Find the values of the following.
$(2 ^{-1}\times4^{-1})\div2^{-2}$
Answer$(2 ^{-1}\times4^{-1})\div2^{-2}$
$=\Big(\frac{1}{2}\times\frac{1}{4}\Big )\div\frac{1}{2^2}$
$=\frac{1}{8}\div\frac{1}{4}=\frac{1}{8}\times\frac{4}{1}=\frac{1}{2}$
View full question & answer→Question 52 Marks
Simplify:
$(4^{-1}-5^{-1})^{-1}\div3^{-1}$
Answer$(4^{-1}-5^{-1})^{-1}\div3^{-1}$
$=\Big(\frac{1}{4}-\frac{1}{5}\Big)^{-1}\times\frac{1}{3}$
$=\Big(\frac{5-4}{20}\Big)^{-1}\times\frac{3}{1}=\Big(\frac{1}{20}\Big)^{-1}\times\frac{3}{1}$
$=\frac{20}{1}\times\frac{3}{1}=60$
View full question & answer→Question 62 Marks
Write the following numbers in the usual form:
$3 \times 10^{-8}$
Answer$3 \times 10^{-8}=\frac{3}{10^8}$
$=\frac{3}{100000000}$
$=0.000000003$
View full question & answer→Question 72 Marks
Simplify:
$(3^{-1}\times4^{-1})^{-1}\times5^{-1}$
Answer$(3^{-1}\times4^{-1})^{-1}\times5^{-1}$
$=\Big(\frac{1}{3}\times\frac{1}{4}\Big)^{-1}\times\frac{1}{5}$
$=\Big(\frac{1}{12}\Big)^{-1}\times\frac{1}{5}=\frac{12}{1}\times\frac{1}{5}=\frac{12}{5}$
View full question & answer→Question 82 Marks
Express the following numbers in standard form:
0.00072984
Answer$0.00072984=\frac{7.2984}{10000}$
$=\frac{7.2984}{10}^{4}=7.2984\times10^{-4}$
View full question & answer→Question 92 Marks
Simplify:
$(3^2-2^2)\times\Big(\frac{2}{3}\Big)^{-3}$
Answer$(3^2-2^2)\times\Big(\frac{2}{3}\Big)^{-3}$
$=(3^{3}-2^3)\times\Big(\frac{3}{2}\Big)^3=(9-4)\times\frac{27}{8}$
$=5\times\frac{27}{8}=\frac{135}{8}$
View full question & answer→Question 102 Marks
Express the following numbers in standard form:
$3759 \times 10^{-4}$
Answer$3759 × 10^{-4}=3.759\times1000\times10 ^{-4}$
$=3.759\times10^3\times10^{-4}$
$=3.759\times10^{-1}$
View full question & answer→Question 112 Marks
Simplify:
$(5^{-1}\div6^{-1} )^3$
Answer$(5^{-1}\div6^{-1})^3=\Big(\frac{1}{5}\div\frac{1}{6}\Big )^3$
$=\Big(\frac{6}{5}\Big)^3=\frac{6\times6\times6}{5\times5\times5}=\frac{216}{125}$
View full question & answer→Question 122 Marks
Write the following numbers in the usual form:
$1.0001 \times 10^9$
Answer$1.0001 × 10^9$
$=1.0001\times1000000000$
$=1000100000$
View full question & answer→Question 132 Marks
Find the values of the following.
$\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$
Answer$\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$
$=(2)^2+(3)^2+(4)^2$
$=4+9+16=29$
View full question & answer→Question 142 Marks
Express the following numbers in standard form:
0.00000000000943
Answer$6020000000000000$
$=9.42\times\frac{1}{1000000000000000}=9.42\times\frac{1}{10^{12}}$
$=9.42\times10^{-12}$
View full question & answer→Question 152 Marks
By what number should $\big(\frac{1}{2}\big) ^{-1}$ be multiplied so that the product may be equal to $\Big(-\frac{4}{7}\Big)^{-1}?$
AnswerLet x be the required number, then
$\text{x}\times\Big(\frac{1}{2}\Big)^{-1}=\Big(\frac{-4}{7}\Big)^{-1}$
$\Rightarrow\text{x}(2)^1=\Big( \frac{-7}{4}\Big)^1$
$\Rightarrow2\text{x}=\frac{-7}{4}$
$\Rightarrow\text{x}=\frac{-7}{4\times2}=\frac{-7}{8}$
$\therefore$ Required number $=\frac{-7}{8}$
View full question & answer→Question 162 Marks
Express the following numbers in standard form:4 ÷ 100000
Answer$4 ÷ 100000$
$=\frac{4}{100000}=\frac{4}{10^5}$
$=4\times10^{-5}$
View full question & answer→Question 172 Marks
Simplify:$(2^{2}+3^2-4^2)\div\Big(\frac{3}{2}\Big)^2$
Answer$(2^{2}+3^2-4^2)\div\Big(\frac{3}{2}\Big)^2$
$=(4\div9-16)\div\frac{9}{4}=-3\times\frac{4}{9}$
$=\frac{-1\times4}{3}=\frac{-4}{3}$
View full question & answer→Question 182 Marks
Write the following numbers in the usual form:
$4.83 \times 10^7$
Answer$4.83 × 10^7$
$=4.83\times100000000$
$=48300000$
View full question & answer→Question 192 Marks
Find x, if
$\Big(\frac{2}{5}\Big)^{-3}\times\Big(\frac{2}{5}\Big)^{15}=\Big(\frac{2}{5}\Big)^{2+3\text{x}}$
Answer$\Big(\frac{2}{5}\Big)^{-3}\times\Big(\frac{2}{5}\Big)^{15}=\Big(\frac{2}{5}\Big)^{2+3\text{x}}$
$\Rightarrow\Big(\frac{2}{5}\Big)^{-3+15}=\Big(\frac{2}{5}\Big)^{2+3\text{x}}$
$\Rightarrow\Big(\frac{2}{5}\Big)^{12}=\Big(\frac{2}{5}\Big)^{2+3\text{x}}$
Comaring, we get:
$2+3\text{x}=12$
$3\text{x}=12-2=10$
$\text{x}=\frac{10}{3}$
View full question & answer→Question 202 Marks
Write the following numbers in the usual form:
$3.02 \times 10^{-6}$
Answer$3.02 × 10-6$
$=\frac{3.02}{10^6}=\frac{3.02}{1000000}$
$=0.000000302$
View full question & answer→Question 212 Marks
Find the values of the following.
$(5^{-1}\times2^{-1})\div6^{-1}$
Answer$(5^{-1}\times2^{-1})\div6^{-1}$
$=\Big(\frac{1}{5}\times\frac{1}{2}\Big)\div\frac{1}{6}$
$=\frac{1}{10}\times\frac{6}{1}=\frac{6}{10}$
$=\frac{6\div2}{10\div2}=\frac{3}{2}$
View full question & answer→Question 222 Marks
Simplify:
$(4^{-1}\times3^{-1})^2$
Answer$(4^{-1}\times3^{-1})^2=\Big(\frac{1}{4}\times\frac{1}{3}\Big)^2=\Big(\frac{1}{12}\Big)^2$
$=\frac{1}{12}\times\frac{1}{12}=\frac{1}{144}$
View full question & answer→Question 232 Marks
Find x, if
$\Big( \frac{1}{4}\Big)^{-4}\times\Big(\frac{1}{4}\Big)^{-8}=\Big(\frac{1}{4}\Big)^{-4\text{x}}$
Answer$\Big( \frac{1}{4}\Big)^{-4}\times\Big(\frac{1}{4}\Big)^{-8}=\Big(\frac{1}{4}\Big)^{-4\text{x}}$
$\Rightarrow\Big(\frac{1}{4}\Big)^{-12}=\Big(\frac{1}{4}\Big)^{-4\text{x}}$
$\Rightarrow\Big(\frac{1}{4}\Big)^{-12}=\Big(\frac{1}{4}\Big)^{-4\text{x}}$
Comparing, we get:
$-4\text{x}=-12\Rightarrow\text{x}=\frac{-12}{-4}=3$
$\therefore\text{x}=3$
View full question & answer→Question 242 Marks
By what number should $5^{-1}$ be multiplied so that the product may be equal to $(-7)^{-1}?$
AnswerLet x be multiplied, the
$\text{x}\times5^{-1}=- (-7)^{-1}$
$\text{x}=\frac{(-7)^{-1}}{ (5)^{-1}}=\Big(\frac{-7}{5}\Big)^{-1}=\Big(\frac{5}{-7}\Big)^1=\frac{-5}{7}$
$\therefore$ Required number $=\frac{-5}{7}$
View full question & answer→Question 252 Marks
Express the following numbers in standard form:
$0.000437 \times 10^4$
Answer$0.000437 × 10^4=\frac{4.37\times10^4}{10000}=\frac{4.37\times10^4}{10^4}$
$=4.37\times10^4\times10^{-4}$
$=4.37\times10^0$
$=4.37\times1=4.37$
View full question & answer→Question 262 Marks
Write the following numbers in the usual form:
$3.25 \times 10^{-7}$
Answer$3.25 × 10^{-7}$
$=\frac{3.25}{10^{7}}=\frac{3.25}{1000000}$
$=0.000000325$
View full question & answer→Question 272 Marks
Express the following numbers in standard form:
6020000000000000
Answer$6020000000000000$
$= 6.02 × 1000000000000000$
$= 6.20 × 1015$
View full question & answer→Question 282 Marks
Simplify:
$(2^{-1}+3^{-1})^{-1}$
Answer$(2^{-1}+3^{-1})^{-1}=\Big(\frac{1}{2}+\frac{1}{3}\Big)^{-1}=\Big(\frac{3+2}{6}\Big)^{-1}$
$=\Big(\frac{5}{6}\Big)^{-1}=\frac{6}{5}$
View full question & answer→Question 292 Marks
Express the following numbers in standard form:
$846 \times 10^7$
Answer$846 × 10^7=8.46\times100\times10^7$
$=8.46\times10^2\times10^7$
$=8.46\times10^9$
View full question & answer→Question 302 Marks
By what number should $5^{-1}$ be multiplied so that the product may be equal to $(-7)^{-1}$ ?
AnswerLet $x$ be multiplied to $5^{-1}$ then
$\text{x}\times5^{-1}=(-7)^{-1}$
$\text{x}\times\frac{1}{5}=\frac{1}{(-7)^1}$
$\Rightarrow\frac{\text{x}}{5}=\frac{1}{-7}$
$\Rightarrow\text{x}=5\times\frac{1}{-7}=\frac{-5}{7}$
$\therefore$ Required number $=\frac{-5}{7}$
View full question & answer→Question 312 Marks
Simplify:
$\bigg[\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\bigg]\div\Big(\frac{1}{4}\Big)^{-3}$
Answer$\bigg[\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\bigg]\div\Big(\frac{1}{4}\Big)^{-3}$
$=(3^{3}-2^3)\div(4)^3$
$=(27-8)\div64=\frac{19}{64}$
View full question & answer→Question 322 Marks
Simplify:
$\bigg\{\Big( \frac{1}{2}\Big )^{-1}\times(-4)^{-1}\bigg\}$
Answer$\bigg\{\Big( \frac{1}{2}\Big )^{-1}\times(-4)^{-1}\bigg\}$
$=\bigg\{\Big(2)^1\times\Big(\frac{1}{-4}\Big)^1\bigg\}=\Big(2\times\frac{1}{-4}\Big)^{-1}$
$=\Big(\frac{-1}{2}\Big)^{-1}=(-2)^1=-2$
View full question & answer→Question 332 Marks
Express the following numbers in standard form:
0.00000000085
Answer$0.00000000085$
$=8.5\times\frac{1}{1000000000000000}=8.5\times\frac{1}{10^{10}}$
$=8.5\times10^{-10}$
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