Question

PLZ HELP!

Rocky simplified an expression in three steps, as shown:


Which is the first incorrect step and why?

Step 1, all the exponents are increased by 2
Step 1, all the exponents are multiplied by 2
Step 2, the exponents in the denominator are added during multiplication
Step 3, the exponents of the same base are added during division

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

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

Explanation:

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

Expression:
`((x^(-5)y^2)/(yx^3\cdot x^3y^(-5)))^2`

Step 1: We will distribute the exponent as:

`(x^(-5* 2)y^(2* 2))/(y^(1* 2)x^(3* 2)\cdot x^(3* 2)y^(-5* 2))`

`(x^(-10)y^(4))/(y^(2)x^(6)\cdot x^(6)y^(-10))`

Step 2: Combine the exponents in denominator.

`(x^(-10)y^(4))/(y^(2+(-10))x^(6+6))`

`(x^(-10)y^(4))/(y^(-8)x^(12))`

Step 3: Use quotient rule of exponents
`(a^m)/(a^n)=a^(m-n)`.

`(x^(-10)y^(4))/(y^(-8)x^(12))=x^((-10-12))y^(4-(-8))`

`(x^(-10)y^(4))/(y^(-8)x^(12))=x^((-22))y^(4+8)`

`(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.