https://file.aiquickdraw.com/mathbot/file/1729623957636tl1fyfph.jpg

In the image, the expression involves several powers, multiplications, and divisions. Let me transcribe it clearly:

\[
(2 \cdot 3)^2 + 2^2 \cdot 5 \cdot \frac{6}{(2^3)} \cdot 2^0 + 3^3 \cdot 4 \cdot 5 \div (3 \cdot 5)^2
\]

Let's break it down step by step:

### Step 1: Solve each power and simplify constants

1. \((2 \cdot 3)^2 = 6^2 = 36\)
2. \(2^2 = 4\)
3. \(2^3 = 8\), so \(\frac{6}{2^3} = \frac{6}{8} = \frac{3}{4}\)
4. \(2^0 = 1\)
5. \(3^3 = 27\)
6. \((3 \cdot 5)^2 = (15)^2 = 225\)

### Step 2: Substitute values into the expression

\[
36 + 4 \cdot 5 \cdot \frac{3}{4} \cdot 1 + 27 \cdot 4 \cdot 5 \div 225
\]

### Step 3: Simplify each term

1. \(36\) (stays the same)
2. \(4 \cdot 5 \cdot \frac{3}{4} \cdot 1 = 5 \cdot 3 = 15\)
3. \(27 \cdot 4 \cdot 5 \div 225 = \frac{27 \cdot 20}{225} = \frac{540}{225} = 2.4\)

### Step 4: Add everything up

\[
36 + 15 + 2.4 = 53.4
\]

So, the result of the entire expression is **53.4**.

Would you like further clarification on any of the steps or details?

### Related Questions:
1. How do you handle exponents with different bases?
2. Can you explain why any number to the power of zero equals one?
3. What is the importance of order of operations (PEMDAS) in expressions like this?
4. How would the result change if the exponent of a term was altered?
5. Can you break down the process of simplifying fractions with exponents in more detail?

### Tip:
Always deal with exponents and powers before performing multiplication and division to avoid mistakes when simplifying expressions.

(2 ⋅ 3)^2 + 2^2 ⋅ 5 ⋅ 6 ÷ (2^3) ⋅ 2^0 + 3^3 ⋅ 4 ⋅ 5 ÷ (3 ⋅ 5)^2

Learn how to simplify the expression (2 ⋅ 3)^2 + 2^2 ⋅ 5 ⋅ 6 ÷ (2^3) ⋅ 2^0 + 3^3 ⋅ 4 ⋅ 5 ÷ (3 ⋅ 5)^2 using exponent rules and the order of operations. Detailed step-by-step solution suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation