Question

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

4 2
4 squared

4
4

16
16

4 16

Answer 1

To evaluate \(4^{9 \cdot 4^{-7}}\), we first simplify the expression inside the exponent.

The exponent can be rewritten as:
\[
9 \cdot 4^{-7} = 9 \cdot \frac{1}{4^7} = \frac{9}{4^7}
\]

Now, substituting this back into the original expression we get:
\[
4^{\frac{9}{4^7}} = 4^{9 \cdot 4^{-7}} = 4^{\frac{9}{4^7}} = 4^{9} \cdot 4^{-7}
\]

Calculating that yields:
\[
4^{9 - 7} = 4^{2}
\]

Thus, the numerical equivalent of the expression \(4^{9 \cdot 4^{-7}}\) simplifies to \(4^2\).

Therefore, the answer is: **4 squared**.