Question

Please help I've been stuck on this question for a while now. How do I solve (1/2)^4 (1/2)^-2? It has to do with Multiplying and Dividing Expressions with Exponents. Please show work so I may figure it out on my own.

Answer 1

The value of the expression is $0.25$

Explanation:

The expression is $\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}$

Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.

Thus, we have,

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

Adding the exponents, we have,

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

Applying exponent rule, $\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$, we have,

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

Simplifying, we get,

$\frac{1}{4}$

Dividing, we have,

$0.25$

Thus, the value of the expression is $0.25$