Math Problem Statement
Simplify the expression, (5 / 5^3)^-1.
Solution
To simplify the expression , let's go through the steps:
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Simplify the fraction inside the parentheses:
So, the expression becomes:
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Apply the power of a power rule: When raising a power to another power, multiply the exponents:
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Calculate :
Thus, the simplified expression is , which corresponds to option a.
Would you like a more detailed explanation or have any other questions?
Here are some related questions to explore:
- How do we handle negative exponents in general?
- What is the power of a quotient rule, and how does it apply here?
- Can you explain the steps for simplifying ?
- How would the solution differ if the exponent were positive, such as ?
- What would happen if the base were a variable instead of a number?
Tip: Remember, raising an expression with a negative exponent to another negative exponent will "flip" it to a positive exponent.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponents
Negative Exponents
Formulas
Power of a power rule
Negative exponent rule
Theorems
Laws of Exponents
Suitable Grade Level
Grades 8-10