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Chapter 2: Problem 25

Simplify. \(\frac{\left(4 d^{9}\right)^{2}}{\left(-2 c^{5}\right)^{6}}\)

Short Answer

Expert verified
The simplified expression is: \[\frac{d^{18}}{4c^{30}}\]

Step by step solution

01

Apply the exponents

First, we can raise each part of the expressions to their respective powers: \[\left(4 d^{9}\right)^{2} = 4^{2}(d^{9})^{2}\] and \[\left(-2 c^{5}\right)^{6} = (-2)^{6}(c^{5})^{6}\]
02

Simplify the exponents

Now, we can simplify the exponents by performing the operations: \[4^{2} = 16\] \[(d^{9})^{2} = d^{18}\] \[(-2)^{6} = 64\] \[(c^{5})^{6} = c^{30}\]
03

Rewrite the fraction with simplified terms

With the simplified exponents, the expression becomes: \[\frac{16d^{18}}{64c^{30}}\]
04

Divide the terms in the fraction

To simplify the fraction further, divide the terms on the numerator and denominator: \[\frac{16d^{18}}{64c^{30}} = \frac{16}{64} \cdot \frac{d^{18}}{c^{30}}\]
05

Simplify the fraction

Finally, we can simplify the fraction by reducing the numerical part and rewriting the simplified expression: \[\frac{16}{64} = \frac{1}{4}\] So, the simplified expression is: \[\frac{1}{4}\cdot \frac{d^{18}}{c^{30}} = \frac{d^{18}}{4c^{30}}\]

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Most popular questions from this chapter

Perform the operation as indicated. Write the final answer without an exponent. \(\frac{-3 \times 10^{5}}{6 \times 10^{8}}\)

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