# How do you write  3x^0 div y^-3 with positive exponents?

Mar 9, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\frac{3 {x}^{0}}{y} ^ - 3$

Then use this rule for exponents to simplify the $x$ term:

${a}^{\textcolor{red}{0}} = 1$

$\frac{3 {x}^{\textcolor{red}{0}}}{y} ^ - 3 \implies \frac{3 \times 1}{y} ^ - 3 \implies \frac{3}{y} ^ - 3$

Then use this rule of exponents to eliminate the negative exponent:

$\frac{1}{x} ^ \textcolor{red}{a} = {x}^{\textcolor{red}{- a}}$

$\frac{3}{y} ^ \textcolor{red}{- 3} \implies 3 {y}^{\textcolor{red}{- - 3}} \implies 3 {y}^{3}$

Mar 9, 2018

$3 {y}^{3}$

#### Explanation:

$3 {x}^{0} \div {y}^{-} 3$

$\therefore = 3 \times 1 \div {y}^{-} 3$

$\therefore = 3 \times \frac{1}{{y}^{-} 3}$

$\therefore = \frac{3}{y} ^ - 3$

$\therefore = 3 {y}^{3}$