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: [tex](\frac{x^{-5}y^2}{yx^3\cdot x^3y^{-5}})^2[/tex]
Step 1: We will distribute the exponent as:
[tex]\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}}[/tex]
[tex]\frac{x^{-10}y^{4}}{y^{2}x^{6}\cdot x^{6}y^{-10}}[/tex]
Step 2: Combine the exponents in denominator.
[tex]\frac{x^{-10}y^{4}}{y^{2+(-10)}x^{6+6}}[/tex]
[tex]\frac{x^{-10}y^{4}}{y^{-8}x^{12}}[/tex]
Step 3: Use quotient rule of exponents [tex]\frac{a^m}{a^n}=a^{m-n}[/tex].
[tex]\frac{x^{-10}y^{4}}{y^{-8}x^{12}}=x^{(-10-12)}y^{4-(-8)}[/tex]
[tex]\frac{x^{-10}y^{4}}{y^{-8}x^{12}}=x^{(-22)}y^{4+8}[/tex]
[tex]\frac{x^{-10}y^{4}}{y^{-8}x^{12}}=x^{(-22)}y^{12}[/tex]
Therefore, the student made a mistake in 3rd step as the exponents of the same base are added during division.
