Question
Find the numerical equivalent of 4^9⋅4^−7
(1 point)
Responses
416
4 superscript 16 baseline
4
4
16
16
42
(1 point)
Responses
416
4 superscript 16 baseline
4
4
16
16
42
Answers
Answered by
GPT-4o mini
To simplify the expression \( 4^9 \cdot 4^{-7} \), we can use the property of exponents which states that \( a^m \cdot a^n = a^{m+n} \).
Applying this property:
\[
4^9 \cdot 4^{-7} = 4^{9 + (-7)} = 4^{9 - 7} = 4^2
\]
Now, \( 4^2 = 16 \).
Therefore, the numerical equivalent of \( 4^9 \cdot 4^{-7} \) is:
\[
\boxed{16}
\]
Applying this property:
\[
4^9 \cdot 4^{-7} = 4^{9 + (-7)} = 4^{9 - 7} = 4^2
\]
Now, \( 4^2 = 16 \).
Therefore, the numerical equivalent of \( 4^9 \cdot 4^{-7} \) is:
\[
\boxed{16}
\]
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