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
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
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