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Chapter 0: Problem 96

Simplify using properties of exponents. $$\left(x^{\frac{4}{5}}\right)^{5}$$

Short Answer

Expert verified
The simplified form of the expression \(\left(x^{\frac{4}{5}}\right)^{5}\) is \(x^4\)

Step by step solution

01

Identify the Expression

Identify the expression that needs simplification, which in this case is \(\left(x^{\frac{4}{5}}\right)^{5}\)
02

Apply the Property of Exponents

Next, apply the exponent property that states when there is an exponent raised to another exponent, they should be multiplied. Hence, the exponents \(\frac{4}{5}\) and 5 are multiplied.
03

Perform the Multiplication

Multiply the exponents together to simplify the expression: \(\frac{4}{5} * 5\)
04

Simplify the Expression

After performing the multiplication, the resulting expression becomes \(x^4\)

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Most popular questions from this chapter

Read the Blitzer Bonus on page \(47 .\) The future is now: You have the opportunity to explore the cosmos in a starship traveling near the speed of light. The experience will enable you to understand the mysteries of the universe in deeply personal ways, transporting you to unimagined levels of knowing and being. The downside: You return from your two-year journey to a futuristic world in which friends and loved ones are long gone. Do you explore space or stay here on Earth? What are the reasons for your choice?

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

a. Find \(\sqrt{16} \cdot \sqrt{4}\) b. Find \(\sqrt{16 \cdot 4}\) c. Based on your answers to parts (a) and (b), what can you conclude?

How do you know if a number is written in scientific notation?
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