Simplify the expression with NO negative exponents.
$2^{-1}+4^{-1}$

• A. $\frac{1}{6}$
• B. $6$
• C. $\frac{3}{4}$
• D. $\frac{4}{3}$

Answer: (C)

Verified step by step guidance

1. Identify the expression to simplify: \$2^{-1} + 4^{-1}$. Negative exponents mean the reciprocal of the base raised to the positive exponent.
2. Rewrite each term with positive exponents by using the rule \(a^{-n} = \frac{1}{a^n}\). So, \(2^{-1} = \frac{1}{2}\) and \(4^{-1} = \frac{1}{4}\).
3. Now the expression becomes \(\frac{1}{2} + \frac{1}{4}\). To add these fractions, find a common denominator. The least common denominator of 2 and 4 is 4.
4. Convert \(\frac{1}{2}\) to an equivalent fraction with denominator 4: \(\frac{1}{2} = \frac{2}{4}\). Now add the fractions: \(\frac{2}{4} + \frac{1}{4}\).
5. Add the numerators while keeping the denominator the same: \(\frac{2 + 1}{4} = \frac{3}{4}\). This is the simplified expression with no negative exponents.