Question

Which expression is equivalent to (r Superscript negative 7 Baseline) Superscript 6?
r Superscript 42
StartFraction 1 Over r Superscript 42 Baseline EndFraction
Negative 7 r Superscript 6
StartFraction 1 Over r EndFraction

Answer 1

To simplify the expression \((r^{-7})^6\), use the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this property:

\[
(r^{-7})^6 = r^{-7 \cdot 6} = r^{-42}
\]

Now, \(r^{-42}\) can be rewritten as:

\[
r^{-42} = \frac{1}{r^{42}}
\]

So, the expression equivalent to \((r^{-7})^6\) is:

\[
\frac{1}{r^{42}}
\]

Therefore, the correct answer is:

\(\frac{1}{r^{42}}\)