Question

use the properties of exponents to rewrite the expression. $(cd^{2})^{3}$
a. $c^{4}d^{5}$
b. $c^{3}d^{6}$
c. $c^{4}d^{6}$
d. $c^{3}d^{2}$
reset selection

Explanation:

Step1: Apply Power of a Product Rule

The power of a product rule states that \((ab)^n = a^n b^n\). For the expression \((cd^2)^3\), we can apply this rule as follows:
\((cd^2)^3 = c^3 \cdot (d^2)^3\)

Step2: Apply Power of a Power Rule

The power of a power rule states that \((a^m)^n = a^{m \cdot n}\). Applying this rule to \((d^2)^3\):
\((d^2)^3 = d^{2 \cdot 3} = d^6\)

Step3: Combine the Results

Substituting \(d^6\) back into the expression from Step 1, we get:
\(c^3 \cdot d^6 = c^3d^6\)

Answer:

B. \(c^3d^6\)