How do you simplify (10k^5v)^3(1/5v^3)^2?

Jun 11, 2018

$\implies 40 {k}^{15} {v}^{9}$

Explanation:

${\left(10 {k}^{5} v\right)}^{3} {\left(\frac{1}{5} {v}^{3}\right)}^{2}$

Quantities with powers raised to powers multiply:

${10}^{3} {k}^{5 \cdot 3} {v}^{3} {\left(\frac{1}{5}\right)}^{2} {v}^{3 \cdot 2}$

$1000 {k}^{15} {v}^{3} \left(\frac{1}{25}\right) {v}^{6}$

Like-terms that are multiplied have their powers summed:

$40 {k}^{15} {v}^{3 + 6}$

$40 {k}^{15} {v}^{9}$