# How do you simplify (6a^-1c^-3)/(d^0)?

Apr 18, 2016

$= \frac{\textcolor{b l u e}{6}}{a {c}^{3}}$

#### Explanation:

$\frac{6 {a}^{-} 1 {c}^{-} 3}{d} ^ 0$

• As per property color(blue)(a^0 =1

(6a^-1c^-3) / d^0 = (6a^-1c^-3) / color(blue)(1

$= 6 {a}^{-} 1 {c}^{-} 3$

• As per property color(blue)(a^-1 =1/a

= 6a^-1c^-3 = 6/ color(blue)((a ^1c^3)

$= \frac{\textcolor{b l u e}{6}}{a {c}^{3}}$

Apr 18, 2016

$\frac{6}{1 {a}^{1} {c}^{3}}$

or

$\frac{6}{a {c}^{3}}$

#### Explanation:

To simplify $\frac{6 {a}^{-} 1 {c}^{-} 3}{d} ^ 0$

We need to eliminate negative exponents and simplify exponents of zero.

In order to simplify negative exponents in the numerator they can be moved to the denominator to make them positive.

${a}^{-} 1 = \frac{1}{a} ^ 1$

${c}^{-} 3 = \frac{1}{c} ^ 3$

Any value to the zero power always equals one.

${d}^{0} = 1$

Therefore the terms convert to

$\frac{6}{1 {a}^{1} {c}^{3}}$

or

$\frac{6}{a {c}^{3}}$