https://file.aiquickdraw.com/mathbot/file/17293445716641zub87x7.jpg

The equation shown in the image is:

\[
x^{\frac{3}{4}} = 8
\]

To solve this equation for \(x\), follow these steps:

### Step 1: Isolate \(x\)
The goal is to remove the exponent \(\frac{3}{4}\) on \(x\). To do this, raise both sides of the equation to the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).

\[
\left( x^{\frac{3}{4}} \right)^{\frac{4}{3}} = 8^{\frac{4}{3}}
\]

This simplifies to:

\[
x = 8^{\frac{4}{3}}
\]

### Step 2: Simplify the Right-Hand Side
To evaluate \(8^{\frac{4}{3}}\), first express 8 as a power of 2:

\[
8 = 2^3
\]

Now substitute this into the equation:

\[
8^{\frac{4}{3}} = (2^3)^{\frac{4}{3}} = 2^4 = 16
\]

### Final Solution:
Thus, the solution is:

\[
x = 16
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:
1. Solve \( x^{\frac{5}{3}} = 32 \).
2. What is the value of \( x \) in \( x^{\frac{2}{3}} = 27 \)?
3. Solve \( (2x)^{\frac{3}{2}} = 64 \).
4. If \( y^{\frac{4}{5}} = 16 \), what is \( y \)?
5. Solve \( 3x^{\frac{2}{3}} = 54 \).

**Tip:** When dealing with fractional exponents, remember that the denominator of the fraction represents the root, and the numerator represents the power.

Learn how to solve the algebraic equation x^(3/4) = 8 using fractional exponents and exponent rules. This detailed solution simplifies the expression and applies exponentiation principles. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation