Math Problem Statement

Evaluate the expression 2^-2*5^3, and give your answer as an integer or a reduced fraction

Solution

To evaluate the expression 22×532^{-2} \times 5^3, follow these steps:

  1. Evaluate each term separately:

    • 222^{-2} is the same as 122=14\frac{1}{2^2} = \frac{1}{4}.
    • 535^3 is 5×5×5=1255 \times 5 \times 5 = 125.
  2. Multiply the results:

    22×53=14×125=12542^{-2} \times 5^3 = \frac{1}{4} \times 125 = \frac{125}{4}

So, the evaluated expression is 1254\frac{125}{4}.

Would you like more information on this topic? Here are some related questions:

  1. How do you simplify expressions with negative exponents?
  2. What is the general rule for multiplying powers?
  3. How do you convert a fraction to a decimal?
  4. What are the steps to simplify a fraction?
  5. Can you convert the fraction 1254\frac{125}{4} into a mixed number?

Tip: When multiplying a fraction by an integer, you can directly multiply the integer with the numerator and keep the denominator the same.

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication of Powers
Negative Exponents
Fraction Operations

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9