Question

Choose all that correctly give an equivalent expression using only positive exponents. x-2y2z-3 = y2 x2z3 x3y-2z4 = x3z4 y2 x-3 y-2z2 = y2 x3z2 x-5 y-4z-2 = y4z2 x5 x3y-4 z-6 = x3z6 y4

Answer 1

1. Correct

2. Correct

3. Incorrect

4. Correct

5. Correct

Explanation:

Recall that:
`a^n=(1)/(a^(-n))` and
`a^(-n)=(1)/(a^n)`

1. The first expression is
`x^(-2)y^2z^(-3)`. We rewrite as positive index to get:

`x^(-2)y^2z^(-3)=(y^2)/(x^2z^3)`

2. The given expression is
`x^3y^(-2)z^(4)=(x^3z^4)/(y^2)`

3. The given expression is:
`x^(-3)y^(-2)z^2=(z^2)/(x^3y^2)`<-------This is the correct expression Not
`x^(-3)y^(-2)z^2=(y^2)/(x^3z^2)`

4. The expression is
`x^(-5)y^(-4)z^(-2)=(1)/(x^5y^4z^2)`

5. The expression is
`x^3y^(-4)z^(-6)=(x^3)/(y^4z^6)`