Math Problem Statement
Use exponent properties to simplify and evaluate the following expression: 5^4 × (5^5 ÷ 5^7)^2 ÷ 5^5.
Solution
Let's solve the given expression step by step:
Problem:
Step 1: Simplify
Using the property of exponents: ,
Step 2: Square the result
Now square :
Step 3: Multiply
Using the property of exponents: ,
Note that .
Step 4: Divide by
Now divide :
Final Answer:
Boxed Answer:
Numerator: , Denominator: .
Do you want a breakdown of these steps, or further clarification? 😊
Related Questions:
- What are the basic exponent rules and how are they applied in simplifying expressions?
- Why does for any nonzero value ?
- How does squaring a term with a negative exponent affect the final result?
- Can this problem be solved without using exponent rules? How would that look?
- How does dividing by a power compare to multiplying by a negative power?
Tip:
When dealing with multiple operations on exponents, always work systematically: simplify powers, apply multiplication/division, and only then deal with fractions or squaring.
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Math Problem Analysis
Mathematical Concepts
Exponent Properties
Simplification of Expressions
Division of Exponents
Negative Exponents
Formulas
a^m ÷ a^n = a^(m-n)
(a^m)^n = a^(m⋅n)
a^m × a^n = a^(m+n)
a^0 = 1
Theorems
Exponent Laws
Suitable Grade Level
Grades 8-10