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Chapter 2: Problem 21

Simplify. \(3 w^{11}\left(7 w^{2}\right)^{2}\left(-w^{6}\right)^{5}\)

Short Answer

Expert verified
The short answer based on the provided step-by-step solution is: \[147w^{45}\]

Step by step solution

01

Evaluate the powers

Evaluate the powers of the numbers inside the parentheses: \((7w^2)^2=(-w^6)^{5}\)
02

Apply the rules for the exponential expression to each term

\( (7w^2)^2 = 7^2 (w^2)^2 = 49w^4\) \((-w^6)^{5} = (-1)^5 (w^6)^{5} = -w^{30}\)
03

Multiply the expression

Multiply the expression using all the simplified terms: \(3w^{11}(49w^4)(-w^{30})\)
04

Apply the product of powers property

To do this, add the exponents of the same base (w) together: \(3w^{11} * 49w^4 * -w^{30} = 3 * 49 * w^{11+4+30} = 147w^{45}\)
05

Write the final simplified expression

The simplified expression is: \[147w^{45}\]

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