Q3. - Algebra 2

Question

Alejandra and Kyle both simplified$\frac{2a^{2}b}{{(-2a{b}^3)}^{-2}}$ . Who is correct? Explain your reasoning.

Step-by-Step Solution

Answer

Alejandra is correct.

Step 1. Write down the given information.

The given expression is $\frac{2a^{2}b}{{(-2a{b}^3)}^{-2}}$ which is solved by both Alejandra and Kyle.

Step 2. Explanation.

The given expression $\frac{2a^{2}b}{{(-2a{b}^3)}^{-2}}$ is solved correctly by Alejandra and Kyle is not correct, because in first step Kyle wrote$\frac{2a^{2}b}{{(-2a{b}^3)}^{-2}}=\frac{2a^{2}b}{{(-2)}^{-2}a{\left(b^3\right)}^{-2}}$ instead of$\frac{2a^{2}b}{{(-2a{b}^3)}^{-2}}=\frac{2a^{2}b}{{(-2)}^{-2}{\left(a\right)}^{-2}{\left(b^3\right)}^{-2}}$ . Therefore, Kyle is incorrect because there should be${\left(a\right)}^{-2}$ in place of$\left(a\right)$ by using the concept of exponents of power property.

Hence, Alejandra is correct.

Step 3. Conclusion.

Alejandra is correct.