# How do you simplify (1/2^-6)(1/2^4)?

Dec 8, 2016

$\left(\frac{1}{2} ^ \left(- 6\right)\right) \left(\frac{1}{2} ^ 4\right)$

Exponents on the denominator of a fraction like these can be written as an exponent with the same base, but an exponent with the opposite sign.
$\frac{1}{2} ^ \left(- 6\right)$ can be rewritten as ${2}^{6}$
$\frac{1}{2} ^ 4$ can be rewritten as ${2}^{- 4}$

$\left(\frac{1}{2} ^ \left(- 6\right)\right) \left(\frac{1}{2} ^ 4\right)$
$= \left({2}^{6}\right) \left({2}^{- 4}\right)$

Use the exponent rule that if exponents with the same base are being multiplied, you can add their exponents:
$= {2}^{2}$
$= 4$