# How do you simplify (-2x^2)^3(4x^3)^-1 ?

Jul 11, 2016

$- 2 {x}^{3}$

#### Explanation:

Rule 1:

${\left({a}^{b}\right)}^{c} = {a}^{b \cdot c}$

Rule 2

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

Rule 3

(a^b)/(a^c) = a^(b-c#


${\left(- 2 {x}^{2}\right)}^{3} {\left(4 {x}^{3}\right)}^{-} 1$

Use rules $1$ and $2$ (mentioned above) of exponents

$\left(- {2}^{3} {x}^{2 \cdot 3}\right) \left(\frac{1}{4 {x}^{3}}\right)$

Simplify by multiplying out the exponents

$\left(- 8 {x}^{6}\right) \left(\frac{1}{4 {x}^{3}}\right)$

Write as fractions

$\frac{- 8 {x}^{6}}{1} \cdot \frac{1}{4 {x}^{3}}$

Rewrite as a single fraction

$\frac{\left(- 8 {x}^{6}\right) \times 1}{1 \times \left(4 {x}^{3}\right)}$

Multiply numerator and denominator by $1$

$\frac{- 8 {x}^{6}}{4 {x}^{3}}$

Simplify coefficients and then simplify variables using rule $3$ from above

$\frac{- 2 {x}^{3}}{1}$

Write without a denominator

$- 2 {x}^{3}$