Math Problem Statement

Simplify the expression \(\frac{x^2 y}{y^{-3}} \times \frac{x^{-4} y^3}{x^{-3}}\)

Solution

The image shows the following expression to be simplified:

x2yy−3×x−4y3x−3\frac{x^2 y}{y^{-3}} \times \frac{x^{-4} y^3}{x^{-3}}

Let's simplify this step by step.

Step 1: Simplify the first fraction

x2yy−3=x2y1−(−3)=x2y4\frac{x^2 y}{y^{-3}} = x^2 y^{1 - (-3)} = x^2 y^{4}

Step 2: Simplify the second fraction

x−4y3x−3=x−4−(−3)y3=x−1y3\frac{x^{-4} y^3}{x^{-3}} = x^{-4 - (-3)} y^3 = x^{-1} y^3

Step 3: Multiply the simplified expressions

x2y4×x−1y3=x2−1y4+3=x1y7x^2 y^{4} \times x^{-1} y^{3} = x^{2 - 1} y^{4 + 3} = x^{1} y^{7}

Thus, the simplified expression is:

xy7x y^7

If you have any questions or need further details, feel free to ask!

Related Questions:

  1. How do you simplify expressions with negative exponents?
  2. What are the rules for multiplying terms with the same base?
  3. How do you handle expressions with multiple variables and exponents?
  4. Can you explain the properties of exponents used in this problem?
  5. How would the solution change if there were more variables in the expression?

Tip: Always simplify expressions within fractions first before multiplying or dividing them to avoid unnecessary complications.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponent Rules
Simplification of Expressions

Formulas

a^m \times a^n = a^{m+n}
\frac{a^m}{a^n} = a^{m-n}
a^{-n} = \frac{1}{a^n}

Theorems

Properties of Exponents

Suitable Grade Level

Grades 9-11

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