# How do you simplify (10^(3/4)*4^(3/4))^(-4)?

Dec 6, 2016

$\frac{1}{64000}$

#### Explanation:

Following the rules for exponents this problem can be rewritten as:

First $\textcolor{red}{{X}^{n} \cdot {Y}^{n} = X {Y}^{n}}$; we can apply this to the terms within parenthesis:

${\left({10}^{\frac{3}{4}} \cdot {4}^{\frac{3}{4}}\right)}^{-} 4 \to {\left({\left(4 \cdot 10\right)}^{\frac{3}{4}}\right)}^{-} 4 \to {\left({40}^{\frac{3}{4}}\right)}^{-} 4$

Next $\textcolor{red}{{\left({X}^{n}\right)}^{m} = {X}^{n \cdot m}}$ can be apply to our simplification:

${\left({40}^{\frac{3}{4}}\right)}^{-} 4 \to {40}^{\left(\frac{3}{4}\right) \cdot - 4} \to {40}^{-} 3$

Finally, $\textcolor{red}{{X}^{-} n = \frac{1}{X} ^ n}$ can applied to give:

${40}^{-} 3 \to \frac{1}{40} ^ 3 \to \frac{1}{40 \cdot 40 \cdot 40} \to \frac{1}{64000}$