Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

Previous problemNext problem

2:25 minutes

Problem 25

Textbook Question

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

Verified step by step guidance

Rewrite each term with a negative exponent using the property of exponents: a^(-n) = 1/(a^n). For the first term, rewrite 2^(-4) as 1/(2^4). For the second term, rewrite 4^(-1) as 1/(4^1).

Simplify the denominators of each fraction. For 1/(2^4), calculate 2^4, which means multiplying 2 by itself 4 times. For 1/(4^1), calculate 4^1, which is simply 4.

Substitute the simplified values of the denominators back into the fractions. This will give you two fractions to add together.

Find a common denominator for the two fractions. The denominators are powers of 2, so determine the least common multiple (LCM) of the denominators.

Rewrite each fraction with the common denominator, then add the numerators together. Simplify the resulting fraction if possible.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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, especially with negative exponents, 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) is equivalent to 1/(a^n). This concept is essential for simplifying expressions with negative exponents, allowing for easier calculations and evaluations of exponential expressions.

Addition of Exponential Terms

When evaluating expressions that involve the addition of exponential terms, it is important to first simplify each term individually before combining them. This involves calculating the value of each exponential expression and then performing the addition. Understanding how to handle these operations is key to accurately solving the given expression.