Question

Which is the simplified form of the expression StartFraction (6 Superscript negative 4 Baseline) Superscript negative 9 Baseline Over 6 Superscript 6 Baseline EndFraction?
StartFraction 1 Over 6 Superscript 42 Baseline EndFraction
StartFraction 1 Over 6 Superscript 19 Baseline EndFraction
6 Superscript 6
6 Superscript 30

Answer 1

To simplify the expression

\[
\frac{(6^{-4})^{-9}}{6^6}
\]

we can start with the numerator, where we have \((6^{-4})^{-9}\).

Using the exponent rule \((a^m)^n = a^{m \cdot n}\):

\[
(6^{-4})^{-9} = 6^{-4 \cdot -9} = 6^{36}
\]

Now, substituting this back into the original expression gives us:

\[
\frac{6^{36}}{6^6}
\]

Now, we can use the quotient rule of exponents \(\frac{a^m}{a^n} = a^{m - n}\):

\[
\frac{6^{36}}{6^6} = 6^{36 - 6} = 6^{30}
\]

Thus, the simplified form of the expression is:

\[
6^{30}
\]

So, the answer is:

\[
6^{30}
\]