Question

Simplify each expression. (10x^3y^2/5x^-3y^4)^-3

Answer 1

When a base with an exponent is divided by a base with an exponent, you subtract the exponents together. (But you can only combine the exponents when the bases are the same)

For example:

`(x^5)/(x^3)=x^((5-3))=x^2`

`(x^3)/(y^6)` (can't combine the exponents because they have different bases of x and y)

`(5^3)/(5^1) =5^((3-1))=5^2=25`

When you multiply an exponent directly to a fraction or a base with an exponent, you multiply the exponents together for each base.

For example:

`(x^4)^2=x^((4*2))=x^8`

`(w^2s^3)^5=w^((2*5))s^((3*5))=w^(10)s^(15)` (multiply the exponent to each base, w and s)

`((x^3)/(y^2))^2=(x^((3*2)))/(y^((2*2))) =(x^6)/(y^4)` (multiply the exponent to each base/top and bottom of the fraction)

When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.

For example:

`x^(-2)` or
`(x^(-2))/(1) =(1)/(x^2)`

`(1)/(2y^(-3))` or
`(1)/(2^1y^(-3)) =(y^3)/(2)`

`((10x^3y^2)/(5x^(-3)y^4) )^(-3)` First simplify the fraction inside the parentheses

`((10)/(5) *x^((3-(-3)))*y^((2-4)))^(-3)`

`(2*x^6*y^(-2))^(-3)` Now multiply the exponents by -3

`2^((1*(-3)))*x^((6*(-3)))*y^((-2*(-3)))`

`2^(-3)x^(-18)y^6` Make all the exponents positive

`(y^6)/(2^3x^(18))` Simplify 2³

`(y^6)/(8x^(18))` [y^6 ÷ 8x^(18)]

Answer 2

y^6/8x^18

Explanation:

Just got it right on Edge2020.