(a2b3)4 Solution

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Jun 07, 2024

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(a2b3)4 Solution: Understanding the Mathematical Expression

In mathematics, algebraic expressions play a crucial role in solving various problems. One such expression is (a2b3)4, which can be daunting for some students. In this article, we will break down the solution to this expression and provide a step-by-step guide to solve it.

What does the expression (a2b3)4 mean?

The expression (a2b3)4 is a mathematical expression that involves exponentiation and multiplication of variables. To understand this expression, let's break it down:

• a and b are variables
• 2 and 3 are exponents (powers) of a and b, respectively
• 4 is the exponent of the entire expression (a2b3)

How to solve (a2b3)4?

To solve this expression, we need to follow the order of operations (PEMDAS):

1. Multiply a and b with their respective exponents: a2 means a to the power of 2, and b3 means b to the power of 3.

a2 = a × a b3 = b × b × b

So, the expression becomes: (a × a × b × b × b)4

2. Raise the entire expression to the power of 4: Now, we need to raise the entire expression (a × a × b × b × b) to the power of 4.

(a × a × b × b × b)4 = (a × a × b × b × b) × (a × a × b × b × b) × (a × a × b × b × b) × (a × a × b × b × b)

Simplified Solution

After simplifying the expression, we get:

(a2b3)4 = a8b12

Here, a is raised to the power of 8, and b is raised to the power of 12.

Conclusion

In conclusion, solving the expression (a2b3)4 involves understanding the order of operations and applying exponentiation rules. By breaking down the expression into smaller parts and applying the correct order of operations, we can arrive at the simplified solution: a8b12.