Question

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

Answer 1

Answer:

64

Step-by-step explanation:

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

The first step is to calculate $(\frac{1}{4})^3$. This is equal to $\frac{1*1*1}{4*4*4}=\frac{1}{64}$. Then, we take the reciprocal. The answer is 64.

Answer 2

Answer:

64

Step-by-step explanation:

Use the definition of a negative exponent.

$a^{-n} = \dfrac{1}{a^n}$

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.

$(\dfrac{1}{4})^{-3} = 4^3 = 64$