Let's solve the equation \( 20^2 = \frac{1}{2} (10h) \) for \( h \).

### Step 1: Simplify the left side
First, calculate \( 20^2 \):
\[
20^2 = 400
\]
So, the equation becomes:
\[
400 = \frac{1}{2} (10h)
\]

### Step 2: Simplify the right side
Distribute \( \frac{1}{2} \) on the right-hand side:
\[
\frac{1}{2} (10h) = 5h
\]
Now the equation is:
\[
400 = 5h
\]

### Step 3: Solve for \( h \)
To isolate \( h \), divide both sides of the equation by 5:
\[
h = \frac{400}{5} = 80
\]

Thus, \( h = 80 \).

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Do you have any questions or would you like more details on a specific step?

Here are 5 related questions to explore:
1. How do you simplify equations with exponents and fractions?
2. How would the equation change if the coefficient of \( h \) were different?
3. What happens if you solve \( 20^3 = \frac{1}{2}(10h) \)?
4. How do you solve for other variables, like \( h \), in different contexts?
5. What is the general method for solving equations involving fractions?

**Tip:** When dealing with fractions, multiplying both sides of the equation by the denominator can help simplify the equation quickly.

This page provides a detailed solution for solving the equation 20² = 1/2(10h). Learn how to simplify exponents, distribute fractions, and solve for h in algebraic equations. Suitable for students in Grades 6-8.

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