Question

Rocky simplified an expression in three steps, as shown:

x to the power of negative 5 multiplied by y to the power of 2, over y multiplied by x to the power of 3 multiplied by x to the power of 3 multiplied by y to the power of negative 5, the whole to the power of 2 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of 2 multiplied by x to the power of 6 multiplied by x to the power of 6 multiplied by y to the power of negative 10 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of negative 8 multiplied by x to the power of 12.

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 three is wrong because when you divide use the quotient rule which is in division the exponents are subtracted and in this problem the exponents are added

Answer 2

Step 3.

Explanation:

The given expression is

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

Step 1: Using distributive property of exponent we get

`((x^(-5))^2(y^2)^2)/((y)^2(x^3)^2\cdot (x^3y^(-5))^2)`
`[\because (ab)^x=a^xb^x]`

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

Ste 2: Using product property of exponent, we get

`(x^(-10)y^4)/(y^(2-10)x^(6+6))`
`[\because a^ma^n=a^(m+n)]`

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

Step 3: Using quotient property of exponent, we get

`x^((-10-12))y^(4-(-8))`
`[\because (a^m)/(a^n)=a^(m-n)]`

`x^((-22))y^(12)`

Therefore, the first incorrect step is 3.