Question

Lauren simplified the expression (m Superscript negative 7 Baseline) Superscript negative 5 as shown.

(m Superscript negative 7 Baseline) Superscript negative 5 = m Superscript negative 7 + (negative 5) Baseline = m Superscript negative 12 Baseline = StartFraction 1 Over m Superscript 12 Baseline EndFraction


Which statement explains Lauren’s error?
She should have subtracted the exponents instead of adding them.
She should have multiplied the exponents instead of adding them.
She should have found –2, not negative 12, as the exponent when she added.
She should have written m Superscript negative 12 as m Superscript 12.

Answer 1

Lauren made an error in her process for simplifying the expression. The correct rule for simplifying an expression with exponents is to **multiply the exponents when raising a power to a power**.

In her case, she should have multiplied -7 and -5 instead of adding them. Therefore, the correct simplification should be:

\[
(m^{-7})^{-5} = m^{-7 \times -5} = m^{35}
\]

Then, to express this in terms of positive exponents:

\[
m^{35} \text{ is already in positive form.}
\]

So the correct statement that explains Lauren's error is:

**She should have multiplied the exponents instead of adding them.**