WeBWorK using host: https://webwork.pcc.edu, format: simple, seed: 2391, course: orcca

We add the exponents because this is a product of powers with the same base:

$\begin{aligned} r^{16}\cdot r^{5}\amp=r^{16+5}\\ \amp=r^{21} \end{aligned}$

We multiply the exponents because this is a power being raised to a power:

$\begin{aligned} \left(x^{11}\right)^{10}\amp=x^{11\cdot10}\\ \amp=x^{110} \end{aligned}$

We apply the power to each factor in the product:

$\begin{aligned} (3r)^{4}\amp=3^4r^4\\ \amp=81r^4 \end{aligned}$

All three exponent rules must be used, one at a time:

$\begin{aligned} \left(3y^2\right)^{2}\left(y^3\right)^5\amp=3^2\left(y^2\right)^2\left(y^3\right)^5\\ \amp=9\left(y^2\right)^2\left(y^3\right)^5\\ \amp=9y^{2\cdot2}y^{3\cdot5}\\ \amp=9y^{4}y^{15}\\ \amp=9y^{4+15}\\ \amp=9y^{19} \end{aligned}$