Math Problem Statement

Simplify the expression, (5 / 5^3)^-1.

Solution

To simplify the expression (553)1\left(\frac{5}{5^3}\right)^{-1}, let's go through the steps:

  1. Simplify the fraction inside the parentheses: 553=513=52\frac{5}{5^3} = 5^{1 - 3} = 5^{-2}

    So, the expression becomes: (52)1(5^{-2})^{-1}

  2. Apply the power of a power rule: When raising a power to another power, multiply the exponents: 52×1=525^{-2 \times -1} = 5^2

  3. Calculate 525^2: 52=255^2 = 25

Thus, the simplified expression is 2525, which corresponds to option a.

Would you like a more detailed explanation or have any other questions?


Here are some related questions to explore:

  1. How do we handle negative exponents in general?
  2. What is the power of a quotient rule, and how does it apply here?
  3. Can you explain the steps for simplifying (aab)1\left(\frac{a}{a^b}\right)^{-1}?
  4. How would the solution differ if the exponent were positive, such as (553)2\left(\frac{5}{5^3}\right)^2?
  5. 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