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

B

Explanation:

Answer 2

She should have multiplied the exponents instead of adding them.

Explanation:

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

• (m⁻⁷)⁻⁵

(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

• (m⁻⁷)⁻⁵ = m⁻⁷⁺⁽⁻⁵⁾ = m⁻¹² = 1/m¹²

Correct solution:

• (nᵃ)ᵇ = nᵃᵇ required property, power of the power is the product of the powers
• (m⁻⁷)⁻⁵ = m⁽⁻⁷⁾⁽⁻⁵⁾ = m³⁵

Correct answer option describing the error made:

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