Respuesta :

maemily738

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 [tex](\frac{1}{4})^3[/tex]. This is equal to [tex]\frac{1*1*1}{4*4*4}=\frac{1}{64}[/tex]. Then, we take the reciprocal. The answer is 64.

mathstudent55

Answer:

64

Step-by-step explanation:

Use the definition of a negative exponent.

[tex] a^{-n} = \dfrac{1}{a^n} [/tex]

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.

[tex] (\dfrac{1}{4})^{-3} = 4^3 = 64 [/tex]

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