/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Simplify. \(5 z^{3}(-4 z)^{2}\... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 22

Simplify. \(5 z^{3}(-4 z)^{2}\left(2 z^{3}\right)^{2}\)

Short Answer

Expert verified
The simplified expression is \(320z^{11}\).

Step by step solution

01

Apply the power rule for exponents

Apply the power rule for exponents to each term within the parentheses: \((-4z)^2 = (-4)^2 \cdot z^2\) and \((2z^3)^2 = 2^2 \cdot z^{3 \cdot 2}\)
02

Square the coefficients and raise the variables to the corresponding powers

Square the coefficients and raise the variables to their corresponding powers: \((-4)^2 = 16\), \(z^2 = z^2\), \(2^2 = 4\), \(z^{3 \cdot 2} = z^6\) Now the expression looks like this: \(5z^3 \cdot 16z^2 \cdot 4z^6\)
03

Multiply coefficients and combine like terms

Multiply the coefficients (5, 16, and 4) and combine the like terms with the same powers of z: \(5 \cdot 16 \cdot 4 = 320\) \(z^3 \cdot z^2 \cdot z^6 = z^{3+2+6} = z^{11}\) Now, the simplified expression is: \(320z^{11}\)

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Most popular questions from this chapter

Simplify the expression using the product rule. Leave your answer in exponential form. $$\left(\frac{5}{3} x^{2}\right)(12 x)\left(-2 x^{3}\right)$$

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Write each number in scientific notation. 0.0008

Perform the operation as indicated. Write the final answer without an exponent. \(\left(-1.5 \times 10^{-8}\right)\left(4 \times 10^{6}\right)\)
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