Sample QuestionsExponents questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Mark $(\checkmark)$ against the correct answer of the following: $\Big(\frac{-1}{3}\Big)^{3}=\ ?$
- A
$\frac{-1}{9}$
- B
$\frac{1}{9}$
- ✓
$\frac{-1}{27}$
- D
$\frac{1}{27}$
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer the following : $0.000367 \times 10^4$ in usual form is:
- ✓
$3.67$
- B
$36.7$
- C
$0.367$
- D
$0.0367$
Answer: A.
View full solution →Tick $(\checkmark)$ the correct answer the following:
$\Big(-\frac{1}{2}\Big)^{3}=\ ?$
- A
$\frac{-1}{6}$
- B
$\frac{1}{6}$
- ✓
$\frac{1}{8}$
- D
$\frac{-1}{8}$
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer the following: The value of $\left(3^{-1}+4^{-1}\right)^{-1} \div 5^{-1}$ is :
- A
$\frac{7}{10}$
- ✓
$\frac{60}{7}$
- C
$\frac{7}{5}$
- D
$\frac{7}{15}$
Answer: B.
View full solution →Mark $(\checkmark)$ against the correct answer of the following: The value of $(-3)^{-3}$ is:
- A
$-27$
- B
$9$
- ✓
$\frac{-1}{27}$
- D
$\frac{1}{27}$
Answer: C.
View full solution →Assertion (A): $2^{3^4}=2^{12}$.
Reason (R): For any integers $a, m$ and $n$, we have $\left(a^m\right)^n=a^{m \times n}$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): $\frac{2^{-100}}{2^{-101}}=2^{-201}$
Reason (R): For any integers $a, m$ and $n$, we have $\frac{a^m}{a^n}=a^{m-n}$
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): $8^{-2}$ is the same as $2^{-8}$.
Reason (R): If $\frac{a}{b}$ be a rational number and $n$ be a positive integer then $\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^n$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): The multiplicative inverse of $a^{-n}$ is $a^n$.
Reason (R): $a^{-n} \times a^n=1$.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Assertion (A): $\frac{2^{-5}}{5^{-2}}=\frac{5^2}{2^5}$.
Reason (R): For any integers $a$ and $n$, we have $a^{-n}=\frac{1}{a^n}$.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Find the value of: $\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$
View full solution →$1$ micron $=\frac{1}{1000000}\text{m}$. Express it in standard form.
View full solution → Evaluate:
$\Bigg\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\Bigg\}\div\Big(\frac{1}{4}\Big)^{-3}$
View full solution →Write the following numbers in usual form:
$6.82 × 10^{-6}$
View full solution →Evaluate: $\Big(\frac{-2}{3}\Big)^{-3}\times\Big(\frac{-2}{3}\Big)^{-2}$
View full solution →By what number should $(-3)^{-1} $ be multiplied so that the product blecomes $ 6^{-1}$?
View full solution →Simplify: $\big(3^{-1}+6^{-1}\big)\div\Big(\frac{3}{4}\Big)^{-1}$
View full solution →Mass of earth is $\left(5.97 \times 10^{24}\right) kg$ and mass of moon is $\left(7.35 \times 10^{22}\right) kg$. What is the total mass of the two?
View full solution →If $5^{2 x+1} \div 25=125$, find the value of $x$.
View full solution →By what number should $(-6)^{-1}$ be multiplied so that the product becomes $9^{-1}$ ?
View full solution →By what number should $\Big(\frac{-2}{3}\Big)^{-3}$ be divided so that the quotient may be $\Big(\frac{4}{27}\Big)^{-2}$?
View full solution →By what number should $\Big(\frac{-2}{3}\Big)^{-3}$ be divided so that the quotient is $\Big(\frac{4}{9}\Big)^{-2}$?
View full solution →In a certain laboratory, scientists grow bacteria for research purposes. During a certain experiment, they rear bacteria in culture in a Petri dish. A particular strain of bacteria doubles in every 30 minutes. The scientists start with a single cell.
(1) How many bacteria will be there in the Petri dish after 12 hours?
(a) $2^{12}$$\quad$(b) $2^{18}$$\quad$(c) $2^{20}$$\quad$(d) $2^{24}$
(2) How many bacteria will be there in the Petri dish after 24 hours?
(a) $2^{24}$$\quad$(b) $2^{36}$$\quad$(c) $2^{40}$$\quad$(d) $2^{48}$
(3) If the Petri dish was full with bacteria after 24 hours, when was it half full?
(a) After 12 hours$\quad$(b) After 18 hours$\quad$(c) After 23 hours$\quad$(d) After 23 hours 30 minutes
(4) Had the scientists started with 1 cell each in two similar Petri dishes, how many bacteria would have been there in all after 12 hours?
(a) $2^{24}$$\quad$(b) $2^{25}$$\quad$(c) $2^{36}$$\quad$(d) $2^{48}$
(5) Had the scientists started with 2 cells in a Petri dish, how much time would they have saved in having a Petri dish full of bacteria?
(a) 30 minutes$\quad$(b) 1 hour$\quad$(c) 6 hours$\quad$(d) 12 hours
View full solution →Evaluate: $\Big(\frac{5}{6}\Big)^{6}\times\Big(\frac{5}{6}\Big)^{-4}$
View full solution →Write the following numbers in usual form:
$3.74 × 10^5$
View full solution →Evaluate: $\Big(\frac{-2}{3}\Big)^{-5}$
View full solution →Fill in the blank.$\Big(\frac{-2}{3}\Big)^{-2}=\ ......$
View full solution →Evaluate: $\Big(\frac{-2}{3}\Big)^{-5}$
View full solution →