Question

Which statements correctly use the properties of exponents to simplify? Check all that apply.

(xy2)2 = x2y4

x3x3 = x6

3y–2 = StartFraction 3 Over y squared EndFraction

2(x2)3 = 8x6

–x2(–x3) = –x6

Answer 1

Expression 1, 2 and 3 uses the correct exponential properties.

Explanation:

Some of the properties of exponents are:

`a^(-m) = \displaystyle(1)/(a^m)\\\\(a^m)^n = a^(mn)\\\\(a^m)/(a^n) = a^(m-n)\\\\a^m* a^n = a^(m+n)`

We have to check the expressions with correct properties of exponent.

Solving can be done in the following manner.

`1.~ (xy^2)^2 = x^2(y^(2* 2)) = x^2y^4\\\\2.~ x^3* x^3 = x^(3+3) = x^6\\\\3.~ 3y^(-2) = 3\displaystyle(1)/(y^2) = (3)/(y^2)\\\\4.~ 2(x^2)^3 = 2(x^(2* 3)) = 2(x^6)=2x^6\\\\5.~ -x^2(-x^3) = x^(2+3) = x^5`

Expression 4 and 5 were wrongly evaluated.