Question

Find the numerical equivalent of 4 to the power of 9⋅4 to the power of −7
(1 point)
Responses

416
4 superscript 16 baseline

42
4 squared

4
4

16

Answer 1

To solve \( 4^9 \cdot 4^{-7} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Applying this property:

\[
4^9 \cdot 4^{-7} = 4^{9 + (-7)} = 4^{9 - 7} = 4^2
\]

Now, we calculate \( 4^2 \):

\[
4^2 = 16
\]

Thus, the numerical equivalent of \( 4^9 \cdot 4^{-7} \) is **16**.