Question

Richard simplified an expression in three steps, as shown:

Which is the first incorrect step and why?

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

Answer 1

Step 2 because Richard multiply the powers of same base in denominator instead adding powers of same base.

Explanation:

We are given that Richard simplified an expression in threes steps

We have to find the incorrect step in simplification of Richard

Step 1: all the exponent are multiplied by 3

`(x^(-4)y^2)/(yx^2\cdot x^2y^(-4))^(3)=(x^(-12)y^6)/(y^3x^6\cdot x^6y^(-12))`

Step 2:The exponents in the denominator are multiplied

`(x^(-12)y^6)/(y^3x^6\cdot x^6 y^(-12))=(x^(-12)y^6)/(x^(12)y^(-9))`

Step 3:The exponents of the same base are subtracted during division

`(x^(-12)y^6)/(x^(12)y^(-9))=x^(-12-12)y^(6+9)`

`=x^(-24)y^(15)`

Richard makes mistake in step 2 when we multiply then power of same base should be added but Richard multiply the powers of same base in denominator.