https://file.aiquickdraw.com/mathbot/file/1727571409895zjhxq18z.jpg

The given expression is:

\[
\frac{(y^3)^5}{(y^8)^7}
\]

Let's simplify it step by step:

### Step 1: Apply the Power of a Power Rule
The power of a power rule states \((x^m)^n = x^{m \cdot n}\). So we apply that to both the numerator and the denominator:

\[
(y^3)^5 = y^{3 \cdot 5} = y^{15}
\]
\[
(y^8)^7 = y^{8 \cdot 7} = y^{56}
\]

Thus, the expression becomes:

\[
\frac{y^{15}}{y^{56}}
\]

### Step 2: Apply the Quotient of Powers Rule
The quotient of powers rule states \(\frac{x^m}{x^n} = x^{m-n}\). Therefore:

\[
\frac{y^{15}}{y^{56}} = y^{15 - 56} = y^{-41}
\]

### Final Answer:
\[
y^{-41}
\]

This can also be written as:

\[
\frac{1}{y^{41}}
\]

Would you like a detailed explanation of any step? 

Here are five related questions to deepen your understanding:

1. How do you apply the power of a power rule in different expressions?
2. What does a negative exponent signify?
3. How do you simplify expressions with different bases in the numerator and denominator?
4. How can fractional exponents be handled similarly to integer exponents?
5. How do exponent rules apply when both powers in the fraction are negative?

**Tip:** When simplifying exponent expressions, always apply the power rules carefully and reduce step by step to avoid errors.

Simplify the expression completely: (y^3)^5 / (y^8)^7

Learn how to simplify the expression (y^3)^5 / (y^8)^7 by applying the power of a power rule and the quotient of powers rule. This step-by-step guide helps students understand exponent rules, ideal for grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation