Math Problem Statement

(-1 1/2)^3 = ?

Solution

The expression provided in the image is:

(112)3\left( -1 \frac{1}{2} \right)^3

This is a mixed fraction, 112-1 \frac{1}{2}, raised to the power of 3. We can first convert the mixed fraction into an improper fraction, then apply the exponent.

Step 1: Convert to an improper fraction

112-1 \frac{1}{2} can be rewritten as 32-\frac{3}{2}.

Step 2: Apply the exponent

We now raise 32-\frac{3}{2} to the power of 3:

(32)3=(3)323=278\left( -\frac{3}{2} \right)^3 = \frac{(-3)^3}{2^3} = \frac{-27}{8}

Thus, the result is:

278\boxed{-\frac{27}{8}}

Would you like any additional explanation or details?

Here are 5 related questions to expand on this:

  1. How do you convert mixed numbers to improper fractions?
  2. What is the general rule for raising a fraction to a power?
  3. How does the negative sign affect the result when raising a number to an odd power?
  4. Can you express 278-\frac{27}{8} as a mixed number?
  5. What happens if the exponent is an even number instead of 3?

Tip: When dealing with mixed numbers, always convert them to improper fractions first to make exponentiation easier.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponentiation
Mixed Numbers
Improper Fractions

Formulas

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

Theorems

Properties of Exponents

Suitable Grade Level

Grades 6-8