Evaluate each exponential expression: 2^(-4) + 4^(-1)

Verified step by step guidance

1. Rewrite the expression using the property of negative exponents: $a^{-n}=\frac{1}{a^n}$.
2. Apply the property to each term: $2^{-4}=\frac{1}{2^4}$ and $4^{-1}=\frac{1}{4^1}$.
3. Calculate the powers: $2^4=16$ and $4^1=4$.
4. Substitute the calculated powers back into the expression: $\frac{1}{16}+\frac{1}{4}$.
5. Find a common denominator to add the fractions: Convert $\frac{1}{4}$ to $\frac{4}{16}$ and then add: $\frac{1}{16}+\frac{4}{16}$.

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form of a^x, where 'a' is a positive constant and 'x' is a variable exponent. These functions exhibit rapid growth or decay depending on the value of 'x'. Understanding how to evaluate these functions is crucial for solving problems involving exponential expressions.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, a^(-n) = 1/(a^n). This concept is essential for simplifying expressions with negative exponents, allowing for easier calculations and evaluations.

Addition of Exponential Terms

When adding exponential terms, it is important to evaluate each term separately before combining them. This involves calculating the value of each exponential expression and then performing the addition. Understanding how to handle different bases and exponents is key to accurately summing these terms.