Question

PLZ HELP!

Answer 1

Step 3 is wrong because when dividing exponents you subtract them x^-10 would be multiplying by x^-12 making it x^-10-12 and that would be x^-22 same applies for the y exponents

Answer 2

Answer:

Step 3: exponents of the same base are added during division.

Step-by-step explanation:

We have been an expression and steps used to solve the expression. We are asked to find the 1st incorrect step.

Expression: $(\frac{x^{-5}y^2}{yx^3\cdot x^3y^{-5}})^2$

Step 1: We will distribute the exponent as:

$\frac{x^{-5\times 2}y^{2\times 2}}{y^{1\times 2}x^{3\times 2}\cdot x^{3\times 2}y^{-5\times 2}}$

$\frac{x^{-10}y^{4}}{y^{2}x^{6}\cdot x^{6}y^{-10}}$

Step 2: Combine the exponents in denominator.

$\frac{x^{-10}y^{4}}{y^{2+(-10)}x^{6+6}}$

$\frac{x^{-10}y^{4}}{y^{-8}x^{12}}$

Step 3: Use quotient rule of exponents $\frac{a^m}{a^n}=a^{m-n}$.

$\frac{x^{-10}y^{4}}{y^{-8}x^{12}}=x^{(-10-12)}y^{4-(-8)}$

$\frac{x^{-10}y^{4}}{y^{-8}x^{12}}=x^{(-22)}y^{4+8}$

$\frac{x^{-10}y^{4}}{y^{-8}x^{12}}=x^{(-22)}y^{12}$

Therefore, the student made a mistake in 3rd step as the exponents of the same base are added during division.