Math Problem Statement
Simplify the expression completely: (y^3)^5 / (y^8)^7
Solution
The given expression is:
Let's simplify it step by step:
Step 1: Apply the Power of a Power Rule
The power of a power rule states . So we apply that to both the numerator and the denominator:
Thus, the expression becomes:
Step 2: Apply the Quotient of Powers Rule
The quotient of powers rule states . Therefore:
Final Answer:
This can also be written as:
Would you like a detailed explanation of any step?
Here are five related questions to deepen your understanding:
- How do you apply the power of a power rule in different expressions?
- What does a negative exponent signify?
- How do you simplify expressions with different bases in the numerator and denominator?
- How can fractional exponents be handled similarly to integer exponents?
- How do exponent rules apply when both powers in the fraction are negative?
Tip: When simplifying exponent expressions, always apply the power rules carefully and reduce step by step to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Exponentiation
Algebra
Simplifying Rational Expressions
Formulas
Power of a power rule: (x^m)^n = x^(m * n)
Quotient of powers rule: (x^m) / (x^n) = x^(m - n)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 8-10