Exponents and Powers

Q. If 3^x = 81, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

81 = 3^4, so x = 4.

Correct Answer: C — 4

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Q. If 4^x = 64, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

64 = 4^3, so x = 3.

Correct Answer: B — 3

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Q. What is the value of (2^3)^2?

A. 2^5
B. 2^6
C. 2^7
D. 2^8

Solution

Using the property (a^m)^n = a^(m*n), we get 2^(3*2) = 2^6.

Correct Answer: B — 2^6

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Q. What is the value of (5^2) * (5^3)?

A. 5^5
B. 5^6
C. 5^7
D. 5^8

Solution

Using the property a^m * a^n = a^(m+n), we get 5^(2+3) = 5^5.

Correct Answer: B — 5^6

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Q. What is the value of 2^5?

A. 8
B. 16
C. 32
D. 64

Solution

2^5 = 2 * 2 * 2 * 2 * 2 = 32.

Correct Answer: C — 32

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Q. What is the value of 5^0 + 5^1 + 5^2?

A. 31
B. 35
C. 36
D. 30

Solution

5^0 = 1, 5^1 = 5, 5^2 = 25. So, 1 + 5 + 25 = 31.

Correct Answer: C — 36

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Q. What is the value of 7^2 * 7^3?

A. 7^4
B. 7^5
C. 7^6
D. 7^7

Solution

Using the property a^m * a^n = a^(m+n), we get 7^(2+3) = 7^5.

Correct Answer: B — 7^5

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Q. What is the value of 9^(1/2)?

A. 3
B. 6
C. 9
D. 18

Solution

9^(1/2) is the square root of 9, which is 3.

Correct Answer: A — 3

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Q. Which of the following is equal to 10^0?

A. 0
B. 1
C. 10
D. 10^1

Solution

Any non-zero number raised to the power of 0 is 1.

Correct Answer: B — 1

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Q. Which of the following is equal to 2^4 / 2^2?

A. 2^2
B. 2^3
C. 2^4
D. 2^5

Solution

Using the property a^m / a^n = a^(m-n), we get 2^(4-2) = 2^2.

Correct Answer: A — 2^2

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Exponents and Powers

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