Math Problem Statement

Select the equivalent expression: (x^2 * x^2 * y) / y^(-4)

Solution

Let's break down the expression provided in the image:

x2x2yy4\frac{x^2 x^2 y}{y^{-4}}

Step-by-step simplification:

  1. Combine like terms:

    • For the xx terms: x2x2=x2+2=x4x^2 \cdot x^2 = x^{2+2} = x^4.
    • The numerator becomes: x4yx^4 y.
  2. Simplify the yy terms:

    • In the denominator, you have y4y^{-4}.
    • Using the property of exponents yy4=y1(4)=y5\frac{y}{y^{-4}} = y^{1 - (-4)} = y^5.

Thus, the simplified expression is:

x4y5x^4 y^5

Now, let's compare it with the options given. The correct equivalent expression is:

x4y5x^4 y^5

So the correct answer is the last option: x4y5x^4 y^5.

Would you like further details or clarifications?

Here are five related questions to consider:

  1. How do you simplify expressions with negative exponents?
  2. What are the rules for multiplying variables with exponents?
  3. How do you simplify a fraction with terms in the numerator and denominator?
  4. Can you explain the property of exponents aman=amn\frac{a^m}{a^n} = a^{m-n}?
  5. What happens when you raise a variable to a zero exponent?

Tip: Always simplify terms with the same base by adding or subtracting their exponents according to their positions (numerator/denominator).

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Simplifying Expressions

Formulas

a^m * a^n = a^(m+n)
y^m / y^n = y^(m-n)
a^(-n) = 1 / a^n

Theorems

Exponent Rules

Suitable Grade Level

Grades 8-10