Question
which expression is equivalent to 7^-3 * 6^-3
1/42^-3
42^-6
42^9
42^-3
1/42^-3
42^-6
42^9
42^-3
Answers
GPT-4o mini
To simplify the expression \( 7^{-3} \times 6^{-3} \), we can rewrite it as follows:
\[
7^{-3} \times 6^{-3} = \frac{1}{7^3} \times \frac{1}{6^3} = \frac{1}{7^3 \times 6^3} = \frac{1}{(7 \times 6)^3} = \frac{1}{42^3}
\]
Now, we need to express this result in terms of the options provided. Since \( \frac{1}{42^3} \) can also be written as \( 42^{-3} \):
The equivalent expression is:
\[
\boxed{42^{-3}}
\]
\[
7^{-3} \times 6^{-3} = \frac{1}{7^3} \times \frac{1}{6^3} = \frac{1}{7^3 \times 6^3} = \frac{1}{(7 \times 6)^3} = \frac{1}{42^3}
\]
Now, we need to express this result in terms of the options provided. Since \( \frac{1}{42^3} \) can also be written as \( 42^{-3} \):
The equivalent expression is:
\[
\boxed{42^{-3}}
\]