Question

which expression is equivalent to 7^-3 * 6^-3
1/42^-3
42^-6
42^9
43^-3

Answer 1

To simplify the expression \( 7^{-3} \times 6^{-3} \), we can rewrite it using properties of exponents:

\[
7^{-3} \times 6^{-3} = (7 \times 6)^{-3}
\]

Calculating \( 7 \times 6 \):

\[
7 \times 6 = 42
\]

Thus, we have:

\[
(7 \times 6)^{-3} = 42^{-3}
\]

Now we can compare this to the options given:

1. \( \frac{1}{42^{-3}} = 42^3 \) (not equivalent)
2. \( 42^{-6} \) (not equivalent)
3. \( 42^9 \) (not equivalent)
4. \( 43^{-3} \) (not equivalent)

The equivalent expression for \( 7^{-3} \times 6^{-3} \) is \( 42^{-3} \). However, that option is not listed.

Thus, the correct equivalent form based on the calculation is:

\[
42^{-3}
\]

None of the provided options match this exactly.