What is a/(\sqrt[6]{b^2)} ?

The solution to a/(\sqrt[6]{b^2)} is (ab^{2/3})/b

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simplify a/(\sqrt[6]{b^2)}

simplify

\frac{a b ^{\frac{2}{3}}}{b}

Solution steps

Multiply by the conjugate

\frac{( b ^{2} ) ^{\frac{5}{6}}}{( b ^{2} ) ^{\frac{5}{6}}}

Simplify

a (b^{2})^{\frac{5}{6}} : a b^{\frac{5}{3}}

= \frac{a b ^{\frac{5}{3}}}{b ^{2}}

b^{\frac{5}{3}} = b^{1 + \frac{2}{3}}, b^{2} = b^{1 + 1}

= \frac{a b ^{\frac{2}{3} + 1}}{b ^{1 + 1}}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

b^{1 + \frac{2}{3}} = b^{1} b^{\frac{2}{3}}, b^{1 + 1} = b^{1} b^{1}

= \frac{a b ^{1} b ^{\frac{2}{3}}}{b ^{1} b ^{1}}

Cancel the common factor:

b^{1}

= \frac{a b ^{\frac{2}{3}}}{b}

12 x - 9 x + 16 - 0.2 x

(x^{2} - 9)^{2} - 9

24 \cdot 28

\frac{175}{30}

8 z - 5 z [4 z - 2 (3 z - 6)] - 7 z (- 5 z + 3)