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Answer 1 · 2017-06-16T05:52:46

$6 a^{3} b^{2} \sqrt{b}$ $6a^3b^2sqrt(b)$

Rewrite as a single problem under a single square root

$= \sqrt{12 a^{5} b 3 a b^{4}}$ $=sqrt(12a^5b3ab^4)$

Rearrange the terms so that like terms are next to each other

$= \sqrt{12 \cdot 3 \cdot a^{5} \cdot a \cdot b \cdot b^{4}}$ $=sqrt(12*3*a^5*a*b*b^4)$

When two exponents with the same base are multiplied, add the exponents under a single base

$= \sqrt{36 \cdot a^{5 + 1} \cdot b^{1 + 4}}$ $=sqrt(36*a^(5+1)*b^(1+4))$

$= \sqrt{36 \cdot a^{6} \cdot b^{5}}$ $=sqrt(36*a^6*b^5)$

An exponent has an exact square root as long as it's divisible by $2$ $2$

$= 6 a^{3} \sqrt{b^{4} b^{1}}$ $=6a^3sqrt(b^4b^1)$

$= 6 x^{3} b^{2} \sqrt{b}$ $=6x^3b^2sqrtb$