Question

Help me please! If you DO decide to help, please explain it to me since I'm extremely confused! THANK YOU!

Answer 1

So firstly, you want to get rid of the outermost powers. The rule with powering something with an exponent is to multiply the exponents together.

In this case:
`(2x^(-2)y)^3=(2^(1*3)x^(-2*3)y^(1*3))=(8x^(-6)y^3)` and
`(4y^3)^2=(4^(1*2)y^(3*2))=(16y^6)`

Our current equation look like this:
`((-4x^2)(8x^(-6)y^3))/((16x^5)(16y^6))`

Next, you want to multiply what's on the numerators and the denominator. The rule with multiplying exponents of the same base is to add them together.

In this case:
`((-4x^2)(8x^(-6)y^3))/((16x^5)(16y^6))=(-32x^(2+(-6))y^3)/(256x^5y^6) =(-32x^(-4)y^3)/(256x^5y^6)`

Now we can divide. The rule with dividing exponents with the same base is that you subtract them.

In this case:
`(-32x^(-4)y^3)/(256x^5y^6)=-(1)/(8) x^(-4-5)y^(3-6)=-(1)/(8) x^(-9)y^(-3)`

Now, if you're required to leave no negative exponents, the rule is that for example x^-2 would turn into 1/x^2. In this case, it would turn like this:
`-(1)/(8x^9y^3)` . And that would be your final answer.

Answer 2

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