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

6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

College Algebra

6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

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0:54 minutes

Problem 5

Textbook Question

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1.5

Verified step by step guidance

Identify the expression to evaluate: $4^{-1.5}$.

Recognize that a negative exponent indicates a reciprocal. Therefore, $4^{-1.5}$ is equivalent to $\frac{1}{4^{1.5}}$.

Rewrite $4^{1.5}$ as $4^{\frac{3}{2}}$, which is the same as $(4^{\frac{1}{2}})^3$.

Calculate $4^{\frac{1}{2}}$, which is the square root of 4, resulting in 2.

Raise the result from the previous step to the power of 3, i.e., $2^3$. Then take the reciprocal of this result to find $4^{-1.5}$.

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Key Concepts

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

Exponents and Powers

Exponents represent repeated multiplication of a base number. In the expression 4^-1.5, the negative exponent indicates the reciprocal of the base raised to the positive exponent. Thus, 4^-1.5 can be rewritten as 1/(4^1.5), which simplifies the calculation process.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy, often to make it simpler or easier to work with. In this case, rounding to three decimal places means keeping three digits after the decimal point and adjusting the last digit based on the value of the next digit.

Using a Calculator for Exponential Functions

Calculators can efficiently compute exponential functions, including those with fractional or negative exponents. To find 4^-1.5, one would input the base and exponent into the calculator, which will provide a decimal approximation that can then be rounded as required.