Math Problem Statement

(2^3+2^3*2^2)/2^3

Solution

Let's break down and simplify the expression step by step:

23+232223\frac{2^3 + 2^3 \cdot 2^2}{2^3}

Step 1: Simplify the powers of 2

  • 23=82^3 = 8
  • 22=42^2 = 4

So the expression becomes:

8+848\frac{8 + 8 \cdot 4}{8}

Step 2: Multiply within the numerator

  • 84=328 \cdot 4 = 32

Now the expression becomes:

8+328\frac{8 + 32}{8}

Step 3: Simplify the addition in the numerator

  • 8+32=408 + 32 = 40

Now the expression is:

408\frac{40}{8}

Step 4: Perform the division

  • 408=5\frac{40}{8} = 5

So, the simplified value of the expression is:

5\boxed{5}

Let me know if you'd like further details or have any questions! Here's a set of related questions:

  1. How do you simplify expressions with exponents in the numerator and denominator?
  2. What is the order of operations when solving expressions involving both exponents and multiplication?
  3. How do you handle terms like 2a2b2^a \cdot 2^b in simplifying expressions?
  4. Can you explain how to use the distributive property to simplify expressions with addition and multiplication?
  5. What happens if the numerator has terms like 2x+2y2^x + 2^y? How would you approach such an expression?

Tip: Always simplify exponents first before doing multiplication or division to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Exponents
Order of Operations
Arithmetic Simplification

Formulas

a^b = a * a * a ... (repeated b times)
(a * b) = ab

Theorems

Order of operations (PEMDAS)

Suitable Grade Level

Grades 6-8