# How do you simplify (a^2bc)^5(a^2bc^5)?

Sep 28, 2015

${a}^{12} \cdot {b}^{6} \cdot {c}^{10}$

#### Explanation:

$\left({a}^{10} \cdot {b}^{5} \cdot {c}^{5}\right) \cdot \left({a}^{2} \cdot b \cdot {c}^{5}\right)$

$\left({a}^{10 + 2}\right) \left({b}^{5 + 1}\right) \left({c}^{5 + 5}\right)$
=${a}^{12} \cdot {b}^{6} \cdot {c}^{10}$

Sep 28, 2015

The answer is ${a}^{12} {b}^{6} {c}^{10}$ .

#### Explanation:

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

Apply the exponent rule ${\left({b}^{n}\right)}^{m} = {b}^{n \cdot m}$ .
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$\left({a}^{2 \cdot 5} {b}^{1 \cdot 5} {c}^{1 \cdot 5}\right) \left({a}^{2} b {c}^{5}\right) =$

$\left({a}^{10} {b}^{5} {c}^{5}\right) \left({a}^{2} b {c}^{5}\right)$

Remove the parentheses and gather like terms.

${a}^{10} {a}^{2} {b}^{5} b {c}^{5} {c}^{5}$

Apply the exponent rule ${a}^{m} \cdot {a}^{n} = {a}^{m + n}$

${a}^{10 + 2} {b}^{5 + 1} {c}^{5 + 5} =$

${a}^{12} {b}^{6} {c}^{10}$