10(a2b3)4 X (10b2)3

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Jun 20, 2024

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Evaluating the Expression: 10(a2b3)4 x (10b2)3

When working with algebraic expressions, it's essential to follow the order of operations (PEMDAS) to ensure accurate calculations. In this article, we'll break down the expression 10(a2b3)4 x (10b2)3 and evaluate it step by step.

Understanding the Expression

The given expression is a product of two terms:

1. 10(a2b3)4
2. (10b2)3

To evaluate this expression, we'll follow the order of operations:

1. Exponents (from right to left)
2. Multiplication and Division (from left to right)
3. Addition and Subtraction (from left to right)

Evaluating the Exponents

Let's start by evaluating the exponents in each term:

Term 1: 10(a2b3)4

• Raise a to the power of 2: a2
• Raise b to the power of 3: b3
• Multiply the results: a2b3
• Raise the product to the power of 4: (a2b3)4 = a8b12

Term 2: (10b2)3

• Raise b to the power of 2: b2
• Multiply 10 by the result: 10b2
• Raise the product to the power of 3: (10b2)3 = 1000b6

Multiplying the Terms

Now that we've evaluated the exponents, we can multiply the two terms:

10(a2b3)4 × (10b2)3 = 10(a8b12) × 1000b6

Simplifying the Expression

To simplify the expression, we can rewrite it as:

10a8b12 × 1000b6 = 10,000a8b18

Thus, the evaluated expression is 10,000a8b18.