Sample QuestionsExponents and Powers questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For any two non-zero rational numbers $x$ and $y$, $x^5 \div y^5$ is equal to
- A
$(x \div y)^1$
- B
$(x \div y)^0$
- ✓
$(x \div y)^5$
- D
$(x \div y)^{10}$
Answer: C.
View full solution →If $\frac{p}{q}=\left(\frac{5}{6}\right)^2 \div\left(\frac{5}{6}\right)^0$, then the value of $\left(\frac{p}{q}\right)^2$ is
- A
$\frac{125}{1290}$
- ✓
$\frac{625}{1296}$
- C
$\frac{164}{125}$
- D
$\frac{169}{144}$
Answer: B.
View full solution →$\left[\left\{\left(\frac{2}{-9}\right)^2\right\}^0\right]^2$ is equal to
- A
- B
$\frac{4}{81}$
- C
$\frac{81}{4}$
- ✓
Answer: D.
View full solution →If $\frac{a}{b}=\left(\frac{625}{81}\right) \div\left(\frac{5^4}{3^4}\right)$, then the value of $\left(\frac{a}{b}\right)^5$ is
Answer: C.
View full solution →If $\left(3^{102} \times 3^{101}\right) \div 3^{101}=k \cdot 3^{100}$, then the value of $k$ is
Answer: A.
View full solution →Assertion (A) When you raise a number to the power of zero, the result is always one.
Reason (R) This is a fundamental property of exponents and holds true for any number.
- ✓
Both A and R are true and R is the correct explanation of A.
- B
Both A and R are true but R is not the correct explanation of A.
- C
A is false but R is true.
- D
A is true but R is false.
Answer: A.
View full solution →Assertion (A) For any two integers $x$ and $y, x^6 \div y^6$ is equal to $\left(\frac{x}{y}\right)^0$.
Reason (R) To divide powers with the same base, keep the base same and subtract the powers.
- A
Both A and R are true and R is the correct explanation of A.
- B
Both A and R are true but R is not the correct explanation of A.
- ✓
A is false but R is true.
- D
A is true but R is false.
Answer: C.
View full solution →Assertion (A) When you multiply numbers with the different base but same exponents, you can add the exponents.
Reason (R) This property is known as the product of powers property in exponents.
- A
Both A and R are true and R is the correct explanation of A.
- B
Both A and R are true but R is not the correct explanation of A.
- ✓
A is false but R is true.
- D
A is true but R is false.
Answer: C.
View full solution →$5^0 \times 25^0 \times 125^0=\left(5^0\right)^6$
View full solution →$4^9$ is greater than $16^3$.
View full solution →$x^0 \times x^0=x^0 \div x^0$ is true for all non-zero values of $x$.
View full solution →$2^0 \times 3^0 \times 0^1 \times 2^{136}=1$
View full solution →$\left(\frac{2}{5}\right)^3 \div\left(\frac{5}{2}\right)^3=1$
View full solution →$88880000000=\ldots . . . \times 10^{10}$
View full solution →$\left(\frac{11}{15}\right)^4 \times$$(\ldots \ldots)^5$ $=\left(\frac{11}{15}\right)^9$
View full solution →If $a^x=1$, then the value of $x$ is $\dots\dots$ ; where $a \neq 1$.
View full solution →$\left(6^4÷6^3\right) \times(1)^{92} \times 2^{36}÷2^{32}=\ldots \ldots$
View full solution →$\left(\frac{-1}{4}\right)^3 \times\left(\frac{-1}{4}\right)^{\cdots}=\left(\frac{-1}{4}\right)^{11}$
View full solution →Using laws of exponents, simplify and write the answer in exponential form.
$8^t÷8^2$
View full solution →Using laws of exponents, simplify and write the answer in exponential form.
$\left(2^{20}÷2^{15}\right) \times 2^3$
View full solution →Using laws of exponents, simplify and write the answer in exponential form.
$a^4 \times b^4$
View full solution →Using laws of exponents, simplify and write the answer in exponential form.
$2^5 \times 5^5$
View full solution →Using laws of exponents, simplify and write the answer in exponential form.
$7^x \times 7^2$
View full solution →Write the following numbers in the expanded forms.
20072
Write the following numbers in the expanded forms.
120719
Write the following numbers in the expanded forms.
2806196
Write the following numbers in the expanded forms.
3006194
Write the following numbers in the expanded forms.
279404
Simplify and write in exponential form.
$\left(\right.$ e.g. $\left.11^6÷11^2=11^4\right)$
(i) $2^9÷2^3$ (ii) $10^8÷10^4$ (iii) $9^{11}÷9^7$
(iv) $20^{15}÷20^{13}$ (v) $7^{13}÷7^{10}$
View full solution →Find five examples, where a number is expressed in exponential form. Also, identify the base and the exponent in each case.
(i) 4096 (il) 216 (iii) 15625 (iv) 1331 (v) 196
Express the following in usual form.
(i) $8.01 \times 10^7$
(ii) $1.75 \times 10^3$
View full solution →If $\frac{p}{q}=\left(\frac{3}{2}\right)^2 \div\left(\frac{9}{4}\right)^0$, then find the value of $\left(\frac{p}{q}\right)^3$.
View full solution →Simplify $\frac{5^2 \times 3^3 \times(125)^{2 / 3}}{(27)^{2 / 3} \times(32)^{1 / 5}}$.
View full solution →Match Column A with Column B.| Column A | Column B |
| (i) $2^0 \times 3^2 \times 4^6 \div 4^2$ | (a) 16 |
| (ii) $\left(\frac{2}{5}\right)^6÷\left(\frac{2}{5}\right)^4$ | (b) $\frac{3}{8}$ |
| (iii) $\left[\left(\frac{3}{4}\right)^6 \div\left(\frac{3}{4}\right)^5\right] \times \frac{1}{2}$ | (c) $\frac{4}{25}$ |
| (iv) $(1)^{200} \times(2)^{198} \div(2)^{194}$ | (d) 2304 |
View full solution →Match Column A with Column B.| Column A | Column B |
| (i) $\left(a^m\right)^n$ | (a) $(a)^{m n}$ |
| (ii) $a^m \div b^m$ | (b) $(a b)^m$ |
| (iii) $a^0$ | (c) $\left(\frac{a}{b}\right)^m$ |
| (iv) $a^m \times b^m$ | (d) 1 |
View full solution →Compare the following numbers.
$2.7 \times 10^{12} ; 1.5 \times 10^8$
View full solution →Express each of the following as product of powers of their prime factors.
648
Express
(i) 729 as a power of 3.
(ii) 128 as a power of 2.
(iii) 343 as a power of 7
Express the following numbers in standard form.
(i) 7647000
(ii) 81900000
(iii) 583000000000
(iv) 24 billion
Express each of the following in single exponential form.
(i) $2^3 \times 3^3$
(ii) $2^4 \times 4^2$
(iii) $5^2 \times 7^2$
(iv) $(-5)^5 \times(-5)$
(v) $(-3)^3 \times(-10)^3$
(vi) $(-11)^2 \times(-2)^2$
View full solution →