Just like most of my students don’t recognize an old-fashioned film strip, they also don’t recognize negative exponents.

Exponents are tricky and they don’t work exactly like other numbers do. Once you learn the exponent rules, you also need to learn how to handle fractional exponents.

## Negative exponents

And the fun doesn’t end there. You also need to understand how negative exponents work. Today a student thought that

\(x^{-2}=-x^2\)

Nope.

Negative exponents work like this:

\(\ x^{-2}=\frac{1}{x^2}\)

The SAT combines all that together into a tricky question. Can you simplify this equation?

\(\ \frac{x^{- \frac{1}{2}}y^3}{x^2 y^{-1}}\)

Move around the negative exponents

\(\ \frac{y \cdot y^3}{x^2 \cdot x^{\frac{1}{2}}}\)

Simplify the top and bottom. Be careful! Remember your exponent rules: When multiplying the same base you ADD the exponents

\(\ \frac{y^{1+3}}{x^{1+ \frac{1}{2}}}\)

\(\ \frac {y^4}{x^{2\frac{1}{2}}}\)

Recognize that

\(\ x^{2\frac{1}{2}} = x^{\frac{5}{2}} \)

So

\(\ \frac{y^4}{x^\frac{5}{2}}\)

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