# Negative Exponents

Negative exponents can be another source of confusion. No matter where you find a negative exponent, you can turn it into a positive exponent by taking the reciprocal of the expression it applies to.

The answer shown below is wrong.  Try working your way through the problem backwards, from the answer up. As you find each mistake, try to identify the thinking behind it… what perspective led to the mistake? What should have been done instead?

$\dfrac{c^{-2}d^3}{c^3d^{-4}}$

$=\dfrac{d^3d^4}{c^{-2}c^3}$

$=\dfrac{d^7}{c^{-6}}$

$=d$

.

..

Hint 1: The correct answer to the original problem is: $\dfrac{d^7}{c^5}$

Hint 2: Several mistakes have been made in the work above – don’t just seek the correct answer – look for the mistakes between every pair of lines.