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

Answer:

1. Correct

2. Correct

3. Incorrect

4. Correct

5. Correct

Step-by-step explanation:

Recall that: $a^n=\frac{1}{a^{-n}}$ and $a^{-n}=\frac{1}{a^n}$

1. The first expression is $x^{-2}y^2z^{-3}$. We rewrite as positive index to get:

$x^{-2}y^2z^{-3}=\frac{y^2}{x^2z^3}$

2.  The given expression is $x^3y^{-2}z^{4}=\frac{x^3z^4}{y^2}$

3. The given expression is: $x^{-3}y^{-2}z^2=\frac{z^2}{x^3y^2}$<-------This is the correct expression Not $x^{-3}y^{-2}z^2=\frac{y^2}{x^3z^2}$

4. The expression is  $x^{-5}y^{-4}z^{-2}=\frac{1}{x^5y^4z^2}$

5. The expression is  $x^3y^{-4}z^{-6}=\frac{x^3}{y^4z^6}$