Math Problem Statement

first question is simplify (1/3²)³

Solution

To simplify (132)3\left(\frac{1}{3^2}\right)^3:

  1. First, calculate the expression inside the parentheses: 132=19\frac{1}{3^2} = \frac{1}{9}

  2. Now, raise 19\frac{1}{9} to the power of 3: (19)3=1393=1729\left(\frac{1}{9}\right)^3 = \frac{1^3}{9^3} = \frac{1}{729}

So, the simplified form of (132)3\left(\frac{1}{3^2}\right)^3 is 1729\frac{1}{729}.

Would you like more details or help with another question? Here are five related questions you might find useful:

  1. How would you simplify (25)4\left(\frac{2}{5}\right)^4?
  2. What is the value of (14)2\left(\frac{1}{4}\right)^2?
  3. Simplify (372)3\left(\frac{3}{7^2}\right)^3.
  4. How do you evaluate (58)2÷(12)\left(\frac{5}{8}\right)^2 \div \left(\frac{1}{2}\right)?
  5. What is (123)2\left(\frac{1}{2^3}\right)^2 in its simplest form?

Tip: When raising a fraction to a power, both the numerator and the denominator are raised to that power separately.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Fractional Powers

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9