Find the numerical equivalent of 4^9 ⋅ 4^−7

Question

options:

4^2

16

4^16

4

Answer 1

To find the numerical equivalent of \( 4^9 \cdot 4^{-7} \), we can use the properties of exponents. Specifically, we use the rule:

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

Applying this rule:

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

Now, we can substitute \( 4^2 \) with its numerical value:

\[ 4^2 = 16 \]

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

So, the answer is: 16