# How do you simplify (4xy)^-1 and write it using only positive exponents?

Mar 25, 2017

$\frac{1}{4 x y}$

#### Explanation:

Permit me to explain using examples

$\textcolor{b l u e}{\text{Example 1}}$

Suppose we had ${b}^{2} / b$

This is the same as $\frac{b \times b}{b} \text{ "=" "b/bxxb" "=" } 1 \times b = b$

Going back to the beginning: Write as ${b}^{2} / {b}^{1}$

No consider ${b}^{2 - 1} = {b}^{1} = b$ so it works to subtract the powers

$\textcolor{b l u e}{\text{Example 2}}$

Suppose we had $\frac{b}{b} ^ 2$

This is the same as $\frac{b}{b \times b} \text{ "=" } \frac{b}{b} \times \frac{1}{b} = \textcolor{red}{\frac{1}{b}}$

No using the method from above

$\frac{b}{b} ^ 2 \text{ "=" "b^(1-2) " "=" } \textcolor{red}{{b}^{- 1}}$

So ${b}^{- 1} = \frac{1}{b} \text{ }$ and using the same principle ${b}^{- 2} = \frac{1}{b} ^ 2$

$\textcolor{b l u e}{\text{Example 3}}$

Not going through the whole demonstration process just accept that: $\frac{1}{b} ^ \left(- 2\right) = {b}^{2}$
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$\textcolor{b l u e}{\text{Answering the question}}$

Using the principles demonstrated above. The power of -1 is applied to everything inside the brackets.

So ${\left(4 x y\right)}^{- 1} = \frac{1}{4 x y}$