Math Problem Statement

Simplify the expression 8x^2 / 3x^5.

Solution

The expression shown in the image is:

8x23x5\frac{8x^2}{3x^5}

To simplify this, follow these steps:

  1. Simplify the coefficients: 83\frac{8}{3} stays as it is since it's already in its simplest form.

  2. Simplify the powers of xx. Use the rule for division of exponents: xaxb=xab\frac{x^a}{x^b} = x^{a-b}. In this case: x2x5=x25=x3\frac{x^2}{x^5} = x^{2-5} = x^{-3}

Thus, the simplified form of the expression is:

83x3\frac{8}{3x^3}

Would you like a more detailed explanation or have any questions?

Here are 5 related questions for further exploration:

  1. How do you simplify expressions with negative exponents?
  2. What is the rule for dividing powers of the same base?
  3. How would the expression change if it were 8x33x5\frac{8x^3}{3x^5}?
  4. What happens if you multiply the simplified expression by x3x^3?
  5. How do you handle expressions with variables in both the numerator and denominator?

Tip: When simplifying algebraic fractions, always reduce the coefficients first, and then apply the exponent rules.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponent Rules

Formulas

x^a / x^b = x^(a-b)

Theorems

Exponent division rule

Suitable Grade Level

Grades 8-10