Question

25 points. What is the value of this expression? 1/4^-3

The “^” means it’s an exponent.



64

12

1/64

1/12

Answer 1

64

Explanation:

Use the definition of a negative exponent.

`a^(-n) = (1)/(a^n)`

A non-zero number, a, raised to the exponent -n equals the reciprocal of the number, 1/a, raised to the exponent n.

Here, a = 1/4. The reciprocal of 1/4 is 4.

Therefore, the number 1/4 raised to -3 is the same as 4 raised to 3.

`((1)/(4))^(-3) = 4^3 = 64`

Answer 2

64

Explanation:

A negative exponent means we first calculate the exponent, then we take the reciprocal.

The first step is to calculate
`((1)/(4))^3`. This is equal to
`(1*1*1)/(4*4*4)=(1)/(64)`. Then, we take the reciprocal. The answer is 64.