Problem 33 Simplify. \(\left(-\frac{2}{5}... [FREE SOLUTION]

Chapter 2: Problem 33

Simplify. \(\left(-\frac{2}{5} c^{9} d^{2}\right)^{3}\left(\frac{5}{4} c d^{6}\right)^{2}\)

Short Answer

Expert verified

\(-\frac{1}{10}c^{29}d^{18}\)

Step by step solution

Applying the exponent rule (Power Rule)

Using the power rule of exponents, when you have a term raised to a power, you multiply the exponents of each factor by that power. So, we will apply this rule to both terms: \[\left(-\frac{2}{5}c^9d^2\right)^3\left(\frac{5}{4}cd^6\right)^2\]

Simplifying each term separately

Now, let's simplify each term individually by raising their parts to the corresponding powers: \[\left(-\frac{2^3}{5^3}c^{9 \times 3}d^{2 \times 3}\right)\left(\frac{5^2}{4^2}c^{1 \times 2}d^{6 \times 2}\right)\] Which simplifies to: \[\left(-\frac{8}{125}c^{27}d^6\right)\left(\frac{25}{16}c^2d^{12}\right)\]

Multiplying the terms together

Now, we multiply the coefficient parts and variables parts of the expression separately: \[-\frac{8}{125} \times \frac{25}{16} \hspace{1cm} c^{27} \times c^2 \hspace{1cm} d^6 \times d^{12}\]

Simplifying the coefficients and variables

Now, let's simplify the coefficients and variables. For the coefficients, we have: \[-\frac{8 \times 25}{125 \times 16}\] For the variables, we will use the rule of exponents for multiplying terms with the same base; we will add their exponents: \[c^{27 + 2} \hspace{1cm} d^{6 + 12}\]

Arriving at the final simplification

After simplifying, we have: \[-\frac{200}{2000}c^{29}d^{18}\] Further simplification results in: \[-\frac{1}{10}c^{29}d^{18}\] So, the simplified expression is: \[-\frac{1}{10}c^{29}d^{18}\]

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91影视

Simplify. \(\left(-\frac{2}{5} c^{9} d^{2}\right)^{3}\left(\frac{5}{4} c d^{6}\right)^{2}\)

Short Answer

Step by step solution

Applying the exponent rule (Power Rule)

Simplifying each term separately

Multiplying the terms together

Simplifying the coefficients and variables

Arriving at the final simplification

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