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Chapter 6: Problem 151

Simplify each expression. $$\left(10 x^{2} y\right)^{3}$$

Short Answer

Expert verified
1000x^{6}y^{3}

Step by step solution

01

Understand the expression

The expression given is \((10x^{2}y)^{3}\). This means we need to raise each part of the term \(10x^{2}y\) to the power of 3.
02

Apply the power to the coefficient

First, apply the exponent to the constant coefficient \(10\): \[10^{3} = 10 \times 10 \times 10 = 1000.\]
03

Apply the power to the variable with exponent

Next, raise \(x^{2}\) to the power of 3: \[(x^{2})^{3} = x^{2 \times 3} = x^{6}.\]
04

Apply the exponent to the remaining variable

Lastly, apply the exponent to the variable \(y\): \[y^{3}.\]
05

Combine all parts

Combine all the parts together: \[1000 x^{6} y^{3}.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Algebraic Expressions
Algebraic expressions involve a combination of numbers, variables, and operations. They can include addition, subtraction, multiplication, division, and exponentiation. In our exercise, the expression \ \(10x^{2}y \)^{3} \ is an example of such an algebraic expression.

When simplifying these expressions, it鈥檚 important to follow the order of operations, also known as PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication/Division (from left to right)
  • Addition/Subtraction (from left to right)

This order helps ensure accurate simplification. Each step taken in solving the given exercise follows this hierarchy. By addressing parentheses and exponents first, we remain consistent in our approach. This ensures accuracy and logical progression in simplifying algebraic expressions.

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Most popular questions from this chapter

Divide each polynomial by the monomial. $$\left(8 x^{3}+6 x^{2}\right) \div 2 x$$

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Simplify. (a) \(\frac{1}{c^{-5}}\) (b) \(\frac{1}{3^{-2}}\)

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