Math Problem Statement

1 4/5³

Solution

To solve 1×(45)31 \times \left(\frac{4}{5}\right)^3, let's follow these steps:

Step 1: Calculate (45)3\left(\frac{4}{5}\right)^3

(45)3=4353=64125\left(\frac{4}{5}\right)^3 = \frac{4^3}{5^3} = \frac{64}{125}

Step 2: Multiply by 1

Since multiplying by 1 does not change the value: 1×64125=641251 \times \frac{64}{125} = \frac{64}{125}

Thus, the result is: 64125\frac{64}{125}

Would you like more details on any step or have additional questions?

Here are 5 related questions to deepen your understanding:

  1. How do you convert a fraction to a decimal?
  2. What happens when you raise a fraction to a negative exponent?
  3. How do you simplify expressions involving powers of fractions?
  4. Can you express 64125\frac{64}{125} as a percentage?
  5. How do you calculate (ab)n\left(\frac{a}{b}\right)^n for any values of aa, bb, and nn?

Tip: Always simplify fractions and perform any power operations before applying other arithmetic operations.

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Math Problem Analysis

Mathematical Concepts

Exponentiation of Fractions
Multiplication of Fractions

Formulas

(a/b)^n = a^n / b^n

Theorems

Exponentiation rules for fractions

Suitable Grade Level

Grades 6-8