Question

use the properties of exponents to rewrite the expression. $(u^{2}v^{4})^{3}$
a. $u^{5}v^{7}$
b. $u^{5}v^{12}$
c. $u^{6}v^{12}$
d. $u^{6}v^{4}$
reset selection

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 \((u^2v^4)^3\), we can apply this rule as follows:
\((u^2v^4)^3=(u^2)^3\cdot(v^4)^3\)

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 each term:
For \((u^2)^3\), we have \(u^{2\times3}=u^6\)
For \((v^4)^3\), we have \(v^{4\times3}=v^{12}\)

Step3: Combine the results

Combining the two results from Step 2, we get \(u^6v^{12}\)

Answer:

C. \(u^6v^{12}\)