Question

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ 2^{-4} $$

Short answer

The simplified form of \(2^{-4}\) is \(\frac{1}{16}\).

Step-by-step solution

Understanding Negative Exponents

A negative exponent is the reciprocal of the base. The term \(2^{-4}\) can be rewritten as \(\frac{1}{2^4}\). This is because the rule for negative exponents is: \(a^{-n} = \frac{1}{a^n}\). Here, 'a' is the base and 'n' is the exponent.

Simplifying the Expression

Rewrite the expression \(\frac{1}{2^4}\). Now calculate the denominator \(2^4 = 2*2*2*2 = 16\). So, \(\frac{1}{2^4} = \frac{1}{16}\).