How do you simplify ${(a^{2} b c)}^{5} (a^{2} b c^{5})$ $(a^2bc)^5(a^2bc^5)$ ?

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How do you simplify ${(a^{2} b c)}^{5} (a^{2} b c^{5})$ $(a^2bc)^5(a^2bc^5)$ ?

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Answer 1 · 2015-09-28T19:14:11

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

Explanation:

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

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

Answer 2 · 2015-09-28T19:51:51

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

Explanation:

${(a^{2} b c)}^{5} (a^{2} b c^{5})$ $(a^2bc)^5(a^2bc^5)$

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

$(a^{10} b^{5} c^{5}) (a^{2} b c^{5})$ $(a^10b^5c^5)(a^2bc^5)$

Remove the parentheses and gather like terms.

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

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

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

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

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How do you simplify ${(a^{2} b c)}^{5} (a^{2} b c^{5})$ $(a^2bc)^5(a^2bc^5)$ ?

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How do you simplify ${(a^{2} b c)}^{5} (a^{2} b c^{5})$ $(a^2bc)^5(a^2bc^5)$ ?