Math Problem Statement

X⁵

Simplify \( \frac{x^5}{x^3} \)

Solution

The given expression is:

x5x3\frac{x^5}{x^3}

To simplify, we apply the laws of exponents. Specifically, the quotient rule for exponents:

xaxb=xab\frac{x^a}{x^b} = x^{a-b}

Using this rule, we subtract the exponents:

x5x3=x53=x2\frac{x^5}{x^3} = x^{5-3} = x^2

So, the simplified expression is:

x2x^2

Would you like more details on exponent rules, or do you have any other questions? Here are some related questions:

  1. How do you simplify an expression with negative exponents?
  2. What happens when you divide powers with the same base and different exponents?
  3. How do you simplify a fraction with exponents that are larger in the denominator?
  4. How can you apply exponent rules to rational expressions?
  5. What are the rules for multiplying terms with exponents?

Tip: Always remember to subtract the exponents when dividing powers with the same base!

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Simplification

Formulas

\( \frac{x^a}{x^b} = x^{a-b} \)

Theorems

Quotient Rule for Exponents

Suitable Grade Level

Grades 6-8