# Basic Exponent Practice with Fractions

## DEFINITIONS: Properties of Exponents

*base*and $\,n\,$ is called the

*exponent*or the

*power*.

If $\,n\in\{1,2,3,\ldots\}\,$, then $$\cssId{s15}{x^n = x\cdot x\cdot x \cdot \ldots \cdot x\,,}$$ where there are $\,n\,$ factors in the product.

In this case, $\,x^n\,$ is just a shorthand for repeated multiplication.

Note that $\,x^1 = x\,$ for all real numbers $\,x\,$.

If $\,x\ne 0\,$, then $\,x^0 = 1\,$.

The expression $\,0^0\,$ is not defined.

If $\,n\in\{1,2,3,\ldots\}\,$ and $\,x\ne 0\,$, then $$ \cssId{s26}{x^{-n}} \cssId{s27}{= \frac{1}{x^n}} \cssId{s28}{= \frac{1}{x\cdot x\cdot x\cdot \ldots \cdot x}}\,, $$ where there are $\,n\,$ factors in the product.

In particular, $\,\displaystyle x^{-1} = \frac{1}{x}\,$ for all nonzero real numbers $\,x\,$. That is, $\,x^{-1}\,$ is the reciprocal of $\,x\,$.

With fractions, it looks like this:

$$\begin{align} \cssId{s36}{(\frac{a}{b})^{-1}}\ &\ \cssId{s37}{= \frac{1}{\frac{a}{b}}} \cssId{s38}{= 1 \div \frac{a}{b}}\cr\cr &\ \cssId{s39}{= 1\cdot\frac{b}{a}} \cssId{s40}{= \frac{b}{a}} \end{align} $$That is, the reciprocal of $\displaystyle\,\frac{a}{b}\,$ is $\displaystyle\,\frac{b}{a}\,$.

Now that you've mired through this calculation once, you'll never have to do it this long way again!

When a fraction is raised to the $\,-1\,$ power,
it just *flips*.
The numerator becomes the new denominator,
and the denominator becomes the new numerator.

## Examples

## Practice

As needed, input your answer as a diagonal fraction (e.g., 2/3), since you can't type horizontal fractions.