Question

Determine the value of the expression
4^3 x 4^-6

.
Responses
A
4^-18
B







1/12
C
negative 64
D







1/64

Answer 1

To determine the value of the expression \( 4^3 \times 4^{-6} \), we can use the exponent rules. Specifically, when multiplying like bases, we add the exponents:

\[
4^3 \times 4^{-6} = 4^{3 + (-6)} = 4^{-3}
\]

Now we can simplify \( 4^{-3} \). The negative exponent indicates that we can take the reciprocal:

\[
4^{-3} = \frac{1}{4^3}
\]

Next, we need to calculate \( 4^3 \):

\[
4^3 = 64
\]

Thus,

\[
4^{-3} = \frac{1}{64}
\]

The value of the expression \( 4^3 \times 4^{-6} \) is \( \frac{1}{64} \).

So, the correct response is:

D) \( \frac{1}{64} \)