Question

use the properties of exponents to rewrite the expression. $(cd^2)^5$
a. $c^6d^7$
b. $c^6d^{10}$
c. $c^5d^2$
d. $c^5d^{10}$
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Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((cd^2)^5\), we can apply this rule to get \(c^5 (d^2)^5\).

Step2: Apply the power of a power rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\). Applying this to \((d^2)^5\), we have \(d^{2\times5}=d^{10}\).

Step3: Combine the results

Combining the results from Step 1 and Step 2, we get \(c^5 d^{10}\).

Answer:

D. \(c^5 d^{10}\)