Question

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

42
4
2
4 squared

416
4
16
4 superscript 16 baseline

16
16

4

Answer 1

To simplify the expression \( 4^9 \cdot 4^{-7} \), you 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 calculate \( 4^2 \):

\[
4^2 = 16
\]

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

The correct response is:

**16**