Find the numerical equivalent of 4 to the power of 9⋅4 to the power of −7

Question

4
16
4 to the power of 16
4 to the power of 2

Answer 1

To find the numerical equivalent of \( 4^9 \cdot 4^{-7} \), we can use the property of exponents that states:

\[ a^m \cdot a^n = a^{m+n} \]

Applying this property to our expression:

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

Now we can evaluate \( 4^2 \):

\[ 4^2 = 16 \]

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

Thus, the answer is \( \text{16} \).