Question

Lola says these two expressions have the same value.

Expression A
Expression B
Left-bracket (StartFraction a Over b EndFraction) Superscript negative 4 Baseline Right-bracket Superscript 0
Left-bracket (StartFraction a Over b EndFraction) Superscript 0 Baseline Right-bracket Superscript negative 4

Which explains whether Lola is correct?
Lola is correct because each expression has a value of 0.
Lola is correct because each expression has a value of 1.
Lola is not correct because the value of expression A is 1 and the value of expression B is (StartFraction b Over a EndFraction) Superscript 4.
Lola is not correct because the value of expression A is (StartFraction b Over a EndFraction) Superscript 4 and the value of expression B is 1.

Answer 1

To evaluate the expressions, let's analyze them step by step.

**Expression A:** \(\left(\frac{a}{b}\right)^{-4}\) and then raised to the power of \(0\):

\[
\left(\left(\frac{a}{b}\right)^{-4}\right)^{0}
\]

Any non-zero number raised to the power of \(0\) is \(1\), so:

\[
\left(\left(\frac{a}{b}\right)^{-4}\right)^{0} = 1
\]

**Expression B:** \(\left(\frac{a}{b}\right)^{0}\) and then raised to the power of \(-4\):

\[
\left(\left(\frac{a}{b}\right)^{0}\right)^{-4}
\]

Again, any non-zero number raised to the power of \(0\) is \(1\), so:

\[
\left(\left(\frac{a}{b}\right)^{0}\right)^{-4} = 1^{-4} = 1
\]

Thus, both expressions evaluate to 1.

Therefore, the correct explanation is:

**Lola is correct because each expression has a value of 1.**