# How do you simplify 3r^-5 using only positive exponents?

Jul 2, 2016

$\frac{3}{x} ^ 5$

#### Explanation:

One of the Laws of Indices states that:

${x}^{-} 1 = \frac{1}{x} \text{ or } {x}^{-} 3 = \frac{1}{x} ^ 3$

Conversely, $\frac{1}{x} ^ - 5 = {x}^{5}$

This means that we can change the sign of an index by moving it from the numerator to the denominator or vice versa.

This cannot happen if there is addition or subtraction!

$3 {r}^{-} 5 = 3 \times {r}^{-} 5 = \frac{3}{x} ^ 5$

Note: The -5 is an index of the r only, so the 3 is not affected.

However, in ${\left(3 r\right)}^{-} 5$ would become $\frac{1}{3 r} ^ 5$