Basic Exponent Practice with Fractions

Let $\,x\in\Bbb{R}\,.$ In the expression $\,x^n\,,$ $\,x\,$ is called the 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 $\,x\,.$