Math Problem Statement

Is the value of the expression greater than 1, equal to 1, or less than 1? (1/5)^3

Solution

The expression shown in the image is (15)3\left(\frac{1}{5}\right)^3.

To evaluate this, let's break it down:

(15)3=1353=1125.\left(\frac{1}{5}\right)^3 = \frac{1^3}{5^3} = \frac{1}{125}.

Now, comparing 1125\frac{1}{125} with 1:

  • 1125\frac{1}{125} is clearly less than 1, as it is a fraction between 0 and 1.

Thus, the value of the expression is less than 1.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

  1. What is the value of (23)3\left(\frac{2}{3}\right)^3?
  2. Is (12)2\left(\frac{1}{2}\right)^2 greater than or less than 1?
  3. How do you simplify (17)4\left(\frac{1}{7}\right)^4?
  4. Compare the values of (34)2\left(\frac{3}{4}\right)^2 and 1.
  5. What is the cube of 25\frac{2}{5}?

Tip: When raising fractions less than 1 to a power, the result becomes smaller the higher the exponent is.

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Math Problem Analysis

Mathematical Concepts

Exponents
Fractions

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8