Negative Exponents

True or false: Any base to the power of 1 equals itself.

• True 

• False

Answer explanation

When you have a number and you raise it to the power of 1, the result is always that same number. For example, if you have the number 5 and raise it to the power of 1 (5¹), the answer is still 5. This is because any number raised to the power of 1 equals itself (a¹ = a).

True or false: Any base (except 0) to the power of 0 equals 0.

• True 

• False

Answer explanation

Raising any nonzero number to the power of 0 results in 1, not 0. For instance, if you have the number 7 and raise it to the power of 0 (7⁰), the answer is 1, not 0. So, the statement is false. The correct rule is that any nonzero base raised to the power of 0 is defined to be 1, not 0 (a⁰ = 1, a ≠ 0).

True or false: Any base (except 0) to a negative exponent is equal to 1 over the base to the positive exponent.

• True

• False

Answer explanation

If you have a nonzero number as a base and a negative exponent, you can rewrite it as 1 over the base raised to the positive version of the exponent. For example, 2^-3 = 1/(2³) = 1/8. Any base (except 0) to a negative exponent is equal to 1 over the base raised to the positive value of the exponent (a^-n) = 1/(aⁿ), a ≠ 0).

What is the value of 13¹?

• 0 

• 1

• 13 

• 169 

Answer explanation

In the expression 13¹, the base is 13, and the exponent is 1. Any number raised to the power of 1 is equal to the number itself. Therefore, 13¹ is equal to 13.

What is the value of 27⁰?

• 0

• 1

• 27

• Undefined

Answer explanation

In any nonzero number raised to the power of 0, the result is always 1. Therefore, 27⁰ is equal to 1.

What is the value of (3)5^-1?

• 5 

• -1/5 

• -5

• 3/5

Answer explanation

In the expression 5^-1, the base is 5, and the exponent is -1. When you see a negative exponent, you can rewrite the expression as 1 over the base raised to the positive value of the exponent. Therefore, 5^-1 is equivalent to 1/(5¹), which equals 1/5. Then, multiply three (3) and one-fifth (1/5): 3 × 1/5 equals 3/5, so (3)5^-1 = 3/5.

What is the value of 0^-1?

• 0 

• 1

• Undefined  

• Infinity

Answer explanation

In the expression 0^-1, the base is 0, and the exponent is -1. When you see a negative exponent, you can rewrite the expression as 1 over the base raised to the positive value of the exponent. So, 0^-1 is equivalent to 1/(0¹), which equals 1/0, but you can’t divide a number by zero, so 0^-1 is undefined.

What is the value of (-8)⁰?

• 0

• -1

• 1 

• -8

Answer explanation

In any nonzero number raised to the power of 0, the result is always 1. Therefore, (-8)⁰ is equal to 1.

What is the value of 7^-2?

• 49

• 1/49 

• -7

• -1/49 

Answer explanation

In the expression 7^-2, the base is 7, and the exponent is -2. When you see a negative exponent, you can rewrite the expression as 1 over the base raised to the positive value of the exponent. Therefore, 7^-2 is equivalent to 1/(7²), which equals 1/49. 

What is the value of (-16)¹?

• 1/16

• 16

• -1/16

• -16

Answer explanation

In the expression (-16)¹, the base is -16, and the exponent is 1. Any number raised to the power of 1 is equal to the number itself. Therefore, (-16)¹ is equal to -16.