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

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Answer 1 · 2018-04-28T04:01:47

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

${(3 a b^{2} c^{5})}^{3} {(a^{3} b^{8} c)}^{2}$ $(3ab^2c^5)^3(a^3b^8c)^2$

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

$3^{3} a^{3} b^{2 \cdot 3} c^{5 \cdot 3} (a^{3 \cdot 2} b^{8 \cdot 2} c^{2}$ $3^3a^3b^(2*3)c^(5*3)(a^(3*2)b^(8*2)c^2$

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

Now combine live variables by adding their exponents.

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

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

How do you simplify (3ab^2c^5)^3(a^3b^8c)^2(3ab2c5)3(a3b8c)2(3ab^2c^5)^3(a^3b^8c)^2?