Solve frac{sqrt[3]{a^4}}{sqrt{b}}frac{sqrt[3]{b}}{sqrt[3]{a^2}}sqrt[3]{asqrt{b}}

$$\frac{ \sqrt[ 3 ]{ { a }^{ 4 } } }{ \sqrt{ b } } \frac{ \sqrt[ 3 ]{ b } }{ \sqrt[ 3 ]{ { a }^{ 2 } } } \sqrt[ 3 ]{ a \sqrt{ b } }$$

Evaluate

$$a$$

Short Solution Steps

Multiply \frac{\sqrt[3]{a^{4}}}{\sqrt{b}} times \frac{\sqrt[3]{b}}{\sqrt[3]{a^{2}}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt[3]{a^{4}}\sqrt[3]{b}}{\sqrt{b}\sqrt[3]{a^{2}}}\sqrt[3]{a\sqrt{b}}$$

Express \frac{\sqrt[3]{a^{4}}\sqrt[3]{b}}{\sqrt{b}\sqrt[3]{a^{2}}}\sqrt[3]{a\sqrt{b}} as a single fraction.

$$\frac{\sqrt[3]{a^{4}}\sqrt[3]{b}\sqrt[3]{a\sqrt{b}}}{\sqrt{b}\sqrt[3]{a^{2}}}$$

Factor the expressions that are not already factored.

$$\frac{\sqrt[3]{b}\sqrt[3]{\sqrt{b}a}\sqrt[3]{a^{4}}}{\sqrt{b}\sqrt[3]{a^{2}}}$$

Cancel out \sqrt[3]{b} in both numerator and denominator.

$$\frac{\sqrt[3]{\sqrt{b}a}\sqrt[3]{a^{4}}}{\sqrt[6]{b}\sqrt[3]{a^{2}}}$$

Expand the expression.

$$\frac{\sqrt[6]{b}a^{\frac{5}{3}}}{\sqrt[6]{b}a^{\frac{2}{3}}}$$

Cancel out \sqrt[6]{b}a^{\frac{2}{3}} in both numerator and denominator.

$$a$$

Differentiate w.r.t. a

$$1$$