# How do you simplify (2^2)^2*(2^3)^-1 and write it using only positive exponents?

Apr 11, 2017

I found $2$

#### Explanation:

We can use some properties of exponents and write it as:
${2}^{2 \cdot 2} / {2}^{3} = {2}^{4} / {2}^{3} = 2$

Where we used the following:
${\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}$
and
${x}^{-} a = \frac{1}{x} ^ a$

Apr 11, 2017

$2$

#### Explanation:

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

$\therefore = \left(2 \cdot 2\right) \cdot \left(2 \cdot 2\right) \cdot {\left(2 \cdot 2 \cdot 2\right)}^{- 1}$

$\therefore = 4 \cdot 4 \cdot {8}^{-} 1$

$\therefore = 16 \cdot \frac{1}{8}$

$\therefore = \frac{16}{8}$

$\therefore = 2$