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.
Which of the following represents the power of product rule?
- A
$(x × y)^a = x^a× y$
- B
$(x × y)^a= x × y^a$
- C
$(x × y)^a= x^a + y^a$
- ✓
$(x × y)^a= x^a× y^a$
Answer: D.
View full solution →The value of $512^\frac{2}{9}$ is:
- A
$\frac{1}{2}$
- B
$2$
- C
$4$
- ✓
$\frac{1}{4}$
Answer: D.
View full solution →Mark $(\checkmark)$ tick against the correct answer in the following:
$\bigg\{6^{-1}+\Big(\frac{3}{2}\Big)^{-1}\bigg\}=?$
- A
$\frac{2}{3}$
- B
$\frac{5}{6}$
- ✓
$\frac{6}{5}$
- D
Answer: C.
View full solution →Simplified value of $(25)^{\frac{1}{3}}\times(5)^{\frac{1}{3}}$ is:
Answer: D.
View full solution →If $x$ varies as the $m^{th}$ power of $y, y$ varies as the $n^{th}$ power of $z$ and $x$ varies as the $p^{th}$ power of $z,$ then which one of the following is correct?
- A
$p = m + n$
- B
$p - m - n$
- ✓
$p - mn$
- D
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The exponential form of $125$ is $5^3$.
Reason: $125 = 5 \times 5 \times 5 = 53$
- ✓
Both assertion and reason are correct and reason is correct explanation for assertion.
- B
Both assertion and reason are correct but reason is correct explanation for assertion.
- C
Assertion is correct but reason is false.
- D
Both assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The exponential form for $8 \times 8 \times 8 \times 8$ taking base as $2$ is $2^{12}$.
Reason: $\left(a^m\right)^n=a^{(m n)}$
- ✓
Both assertion and reason are correct and reason is correct explanation for assertion.
- B
Both assertion and reason are correct but reason is correct explanation for assertion.
- C
Assertion is correct but reason is false.
- D
Both assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $5^8 \div 5^9=5^8-9=5^{(-1)}$
Reason: In division base is same then subtraction of exponents
- ✓
Both assertion and reason are correct and reason is correct explanation for assertion.
- B
Both assertion and reason are correct but reason is correct explanation for assertion.
- C
Assertion is correct but reason is false.
- D
Both assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R) $have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $(-1)^4=(-1)$
Reason: $(-1)$ raised to any even power is $(+1)$
- ✓
Both assertion and reason are correct and reason is correct explanation for assertion.
- B
Both assertion and reason are correct but reason is correct explanation for assertion.
- C
Assertion is correct but reason is false.
- D
Both assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the exponent is $0$, then we get $1$ as the final result
Reason: $9^{0=1}$
- ✓
Both assertion and reason are correct and reason is correct explanation for assertion.
- B
Both assertion and reason are correct but reason is correct explanation for assertion.
- C
Assertion is correct but reason is false.
- D
Both assertion and reason are false.
Answer: A.
View full solution →A negative number raised to even power is a positive number.
$2^3 \times 3^2=6^5$.
View full solution →$2^3>5^2$.
View full solution →$5^0=(1500)^0$.
View full solution →$10 \times 10^{11}=100^{11}$.
View full solution →The standard form of $27.345$ is $…………. \left(2.7345 \times 10^1, 2.7345 \times 10^2, 2.7345 \times 10^3\right)$
View full solution →$(3785)^0=………… (37850, 3785, 1)$
View full solution →$(-1)^{17}=………… (1, (- 1), (- 17)]$
View full solution →$(25)^0 \times 5^2=…………… (25. 1. 0)$
View full solution →$\left(3^3\right)^2=$………… $\left(2^5, 3^6, 3^5\right)$
View full solution →Express the number appearing in the statement in standard form. The earth has $1,353,000,000$ cubic km of sea water.
View full solution →Express the number appearing in the statement in standard form: $60,230, 000,000,000,000,000,000$ molecules are contained in a drop of water weighting $1.8 gm.$
View full solution →Express the number appearing in the statement in standard form: The universe is estimated to be about $12,000,000,000$ years old.
View full solution →Express the number appearing in a statement in standard form. In a galaxy, there are on an average $100,000,000,000$ stars.
View full solution →Express the number appearing in the following statements in standard form. Diameter of the Sun is $1,400,000,000 m.$
View full solution →Express the number appearing in the statement in standard form: The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be $300,000,000,000,000,000,000\ m.$
View full solution →Simplify:$\frac{3^{5} \times 10^{5} \times 25}{5^{7} \times 6^{5}}$
View full solution →Simplify:$\frac{25 \times 5^{2} \times t^{8}}{10^{3} t^{4}}$
View full solution →Simplify $\frac{\left(2^{5}\right)^{2} \times 7^{3}}{8^{3} \times 7}$
View full solution →Express a product of prime factor only in exponential form: $768$
View full solution →Expand $a^3 b^2, a^2 b^3, b^2 a^3, b^3 a^2$ . Are they all same?
View full solution →A light-year is the distance light travels in one Earth year. For objects in space, we use light years to describe the distance between two heavenly bodies.
One light-year is approximately $9,500,000,000,000\ km.$
$1.$ Express one light year in metres.
$2.$ Astronomers are observing a star that is $5$ light-years away from the Earth. How far is the star from the Earth in kilometres$?$
$A. 4.75 \times 10^{11}$
$B. 47.5 \times 10^{11}$
$C. 4.75 \times 10^{12}$
$D. 4.75 \times 10^{13}$
View full solution →Nanoscience is the study of structures and materials of an ultra-small scale. The widely used
units to measure length in nanoscience are nanometre and micrometre.
The relations between different units of length are given below.
$10^3$ nanometre $(nm) = 1$ micrometre $(µm)$
$10^6$ nanometre $(nm) = 1$ millimetre $(mm)$
$10^7$ nanometre $(nm) = 1$ centimetre $(cm)$
$10^9$ nanometre $(nm) = 1$ meter $(m)$
$1.$ Electron microscopes are used to see very small particles. These microscopes can enlarge an image up to $106$ times. A laboratory developed a switch that is $1$ nanometre wide. How wide will the switch look when seen under an electron microscope$?$
$A. 1$ nanometre
$B. 1$ micrometre
$C. 1$ millimetre
$D. 1$ centimetre
$2.$ Asha measures the thickness of one sheet of newspaper. A stack of $100$ sheets of newspaper is $1\ cm$ thick. What would be the thickness of the newspaper when expressed in nanometres?
$3.$ Scalpel is an instrument used by surgeons in surgery. During an experiment it was found that the size of tip of scalpel can affect the recovery rates of patients.
Two scalpels of tip sizes $0.8$ micrometre and $12.5$ micrometre were tested.
Patients on whom the scalpel with tip radius $0.8$ micrometre was used healed faster.
What is the difference between the radii of the two tips in millimetres$?$
$A. 1.6 \times 10^{-4}$
$B.0.8 \times 10^{-3}$
$C. 1.17 \times 10^{-2}$
$D. 4.5 \times 10^{-2}$
$4.$ Deoxyribonucleic acid $(DNA)$ is found in every cell of almost all living beings including humans. One strand of human $DNA $ is $2.5$ nanometres in diameter. What is the diameter of the strand of $DNA$ in meters$?$
$A. 2.5 \times 10^{-10}$
$B. 1 \times 10^{-9}$
$C. 2.5 \times 10^{-9}$
$D. 2.5 \times 10^9$
$5$. Research says, “Human fingernail grows one nanometre in one second.”
What would be the approximate growth of the fingernail (in cm) in $24$ hours?
$A. 8.64 \times 10^{-3}$
$B.8.64 \times 10^{-2}$
$C. 8.64 \times 10^3$
$D. 8.64 \times 10^{11}$
$6.$ Rajat claims, “A negative number raised to a power is always less than the number itself.” Give an example that proves that Rajat is incorrect.
$7.$ Simplify the following.
$\{(92)^4× 9^5\} ÷ 9^8$
$8.$ Assume x and y are two negative numbers. ‘The result of the multiplication of $x$ and $y$ with the same positive power is greater than the multiplication of $x$ and $y$ with the same negative power.’
Give an example to support this statement.
View full solution →Nanoscience is the study of structures and materials of an ultra-small scale. The widely used
units to measure length in nanoscience are nanometre and micrometre.
The relations between different units of length are given below.
10³ nanometre (nm) = 1 micrometre (µm)
10⁶ nanometre (nm) = 1 millimetre (mm)
10⁷ nanometre (nm) = 1 centimetre (cm)
10⁹ nanometre (nm) = 1 meter (m)
1. Research says, “Human fingernail grows one nanometre in one second.”
What would be the approximate growth of the fingernail (in cm) in 24 hours?
A. $8.64 \times 10^{-3}$
B. $8.64 \times 10^{-2}$
C. $8.64 \times 10^3$
D. $8.64 \times 10^{11}$
2. Rajat claims, “A negative number raised to a power is always less than the number itself.” Give an example that proves that Rajat is incorrect.
3. Simplify the following.
{(92)⁴× 9⁵} ÷ 9⁸
4. Assume x and y are two negative numbers. ‘The result of the multiplication of x and y with the same positive power is greater than the multiplication of x and y with the same negative power.’
Give an example to support this statement.
View full solution →Simplify and express in exponential form: $\left[\left(5^{2}\right)^{3} \times 5^{4}\right] \div 5^{7}$
View full solution →Simplify and express in exponential form: $\frac{2^{3} \times 3^{4} \times 4}{3 \times 32}$
View full solution →Work out $(1)^5,(-1)^3,(-1)^4,(-10)^3,(-5)^4$.
View full solution →