Please help/show work.18 **Solve the equation $ x^{\frac{5}{4}} = 32 $**To solve the equation $ x^{\frac{5}{4}} = 32 $, follow these steps:1. **Isolate the variable:** In this case, the variable $ x $ is already isolated. 2. **Eliminate the fractional exponent:** Raise both sides of the equation to the reciprocal of $ \frac{5}{4} $. The reciprocal of $ \frac{5}{4} $ is $ \frac{4}{5} $. $ (x^{\frac{5}{4}})^{\frac{4}{5}} = 32^{\frac{4}{5}} $3. **Simplify the left side:** The left side simplifies to $ x $. $ x = 32^{\frac{4}{5}} $4. **Evaluate the right side:** To find $ 32^{\frac{4}{5}} $, start by expressing 32 as a power of 2. $ 32 = 2^5 $ Substitute into the equation: $ 32^{\frac{4}{5}} = (2^5)^{\frac{4}{5}} $ Use the property of exponents: $ (2^5)^{\frac{4}{5}} = 2^{5 \cdot \frac{4}{5}} $ Simplify the exponent: $ 2^{5 \cdot \frac{4}{5}} = 2^4 $ Calculate: $ 2^4 = 16 $Therefore, the solution to the equation $ x^{\frac{5}{4}} = 32 $ is $ x = 16 $.---Use this approach and steps to solve similar fractional exponent equations. Make sure you are comfortable with exponent rules and fractional exponents to solve these types of problems correctly.

Name: Please help/show work.18 **Solve the equation $ x^{\frac{5}{4}} = 32
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Description: Please help/show work.18 **Solve the equation \( x^{\frac{5}{4}} = 32 $**To solve the equation $ x^{\frac{5}{4}} = 32 $, follow these steps:1. **Isolate the variable:** In this case, the variable $ x $ is already isolated. 2. **Eliminate the

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Answered: 5. Solve the equation x4 = 32.

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Algebra

5. Solve the equation x4 = 32.

Algebra and Trigonometry (6th Edition)

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ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

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A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

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Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

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Question

Please help/show work.18

**Solve the equation $ x^{\frac{5}{4}} = 32 $**

To solve the equation $ x^{\frac{5}{4}} = 32 $, follow these steps:

1. **Isolate the variable:**
In this case, the variable $ x $ is already isolated.

2. **Eliminate the fractional exponent:**
Raise both sides of the equation to the reciprocal of $ \frac{5}{4} $. The reciprocal of $ \frac{5}{4} $ is $ \frac{4}{5} $.
$ (x^{\frac{5}{4}})^{\frac{4}{5}} = 32^{\frac{4}{5}} $

3. **Simplify the left side:**
The left side simplifies to $ x $.
$ x = 32^{\frac{4}{5}} $

4. **Evaluate the right side:**
To find $ 32^{\frac{4}{5}} $, start by expressing 32 as a power of 2.
$ 32 = 2^5 $
Substitute into the equation:
$ 32^{\frac{4}{5}} = (2^5)^{\frac{4}{5}} $
Use the property of exponents:
$ (2^5)^{\frac{4}{5}} = 2^{5 \cdot \frac{4}{5}} $
Simplify the exponent:
$ 2^{5 \cdot \frac{4}{5}} = 2^4 $
Calculate:
$ 2^4 = 16 $

Therefore, the solution to the equation $ x^{\frac{5}{4}} = 32 $ is $ x = 16 $.

---

Use this approach and steps to solve similar fractional exponent equations. Make sure you are comfortable with exponent rules and fractional exponents to solve these types of problems correctly.

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