# How do you simplify (3ab^2c^5)^3(a^3b^8c)^2?

Apr 28, 2018

$27 {a}^{9} {b}^{22} {c}^{17}$

#### Explanation:

${\left(3 a {b}^{2} {c}^{5}\right)}^{3} {\left({a}^{3} {b}^{8} c\right)}^{2}$

To simplify begin by distributing the exponents outside the parenthesis to each of the terms inside the parenthesis multiplying by each exponent.

3^3a^3b^(2*3)c^(5*3)(a^(3*2)b^(8*2)c^2

$27 {a}^{3} {b}^{6} {c}^{15} {a}^{6} {b}^{16} {c}^{2}$

Now combine live variables by adding their exponents.

$27 {a}^{3 + 6} {b}^{6 + 16} {c}^{15 + 2}$

$27 {a}^{9} {b}^{22} {c}^{17}$