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:
Step-by-step simplification:
-
Combine like terms:
- For the terms: .
- The numerator becomes: .
-
Simplify the terms:
- In the denominator, you have .
- Using the property of exponents .
Thus, the simplified expression is:
Now, let's compare it with the options given. The correct equivalent expression is:
So the correct answer is the last option: .
Would you like further details or clarifications?
Here are five related questions to consider:
- How do you simplify expressions with negative exponents?
- What are the rules for multiplying variables with exponents?
- How do you simplify a fraction with terms in the numerator and denominator?
- Can you explain the property of exponents ?
- 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