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Chapter 2: Problem 38

Simplify. \(\left(\frac{2 p r^{8}}{q^{11}}\right)^{5}\)

Short Answer

Expert verified
The simplified expression is: \(\frac{32p^5 r^{40}}{q^{55}}\)

Step by step solution

01

Distributing the Exponent

Distribute the exponent of 5 to each term inside the parentheses, which includes: 2, \(p\), \(r^8\), and \(q^{11}\). Remember, when raising a power to another power, we multiply the exponents.
02

Applying exponent rules

Apply the exponent rules to each term: \(2^5 = 32\) \(p^5\) \(r^{8\cdot5} = r^{40}\) \(q^{11\cdot5} = q^{55}\)
03

Combine terms

Combine the terms from step 2, placing the numerator terms on top and the denominator terms on bottom: \[\frac{32p^5r^{40}}{q^{55}}\] The simplified expression is: \(\frac{32p^5 r^{40}}{q^{55}}\)

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Most popular questions from this chapter

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Write each number in scientific notation. -145,000

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