Math Problem Statement

2^{-3} + \frac{1}{2^3}

Solution

The given expression is:

23+1232^{-3} + \frac{1}{2^3}

Step 1: Simplify 232^{-3}

Using the property of exponents: 23=123=182^{-3} = \frac{1}{2^3} = \frac{1}{8}

Step 2: Simplify 123\frac{1}{2^3}

This is already in its simplest form: 123=18\frac{1}{2^3} = \frac{1}{8}

Step 3: Add the two terms

Now, we add the two fractions: 18+18=28=14\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}

Final Answer:

The simplified result is: 14\boxed{\frac{1}{4}}

Would you like further details or have any questions?

Here are 5 related questions for practice:

  1. What is the value of 22+1222^{-2} + \frac{1}{2^2}?
  2. How do you simplify 32+1323^{-2} + \frac{1}{3^2}?
  3. What is 51+1515^{-1} + \frac{1}{5^1}?
  4. How can you express 24+1242^{-4} + \frac{1}{2^4}?
  5. What is the result of 42+1424^{-2} + \frac{1}{4^2}?

Tip: When dealing with negative exponents, always remember that an=1ana^{-n} = \frac{1}{a^n}.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponents
Fractions
Negative Exponents

Formulas

a^{-n} = \frac{1}{a^n}

Theorems

-

Suitable Grade Level

Grades 7-9