Solve (2x^4y^frac{-1{5}})(8y^2)^frac{2{3}}

$$( 2 x ^ { 4 } y ^ { \frac { - 1 } { 5 } } ) ( 8 y ^ { 2 } ) ^ { \frac { 2 } { 3 } }$$

Evaluate

$$8y^{\frac{17}{15}}x^{4}$$

Solution Steps

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$2x^{4}y^{-\frac{1}{5}}\times \left(8y^{2}\right)^{\frac{2}{3}}$$

Expand \left(8y^{2}\right)^{\frac{2}{3}}.

$$2x^{4}y^{-\frac{1}{5}}\times 8^{\frac{2}{3}}\left(y^{2}\right)^{\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{2}{3} to get \frac{4}{3}.

$$2x^{4}y^{-\frac{1}{5}}\times 8^{\frac{2}{3}}y^{\frac{4}{3}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$2x^{4}y^{-\frac{1}{5}}\times 4y^{\frac{4}{3}}$$

Multiply 2 and 4 to get 8.

$$8x^{4}y^{-\frac{1}{5}}y^{\frac{4}{3}}$$

To multiply powers of the same base, add their exponents. Add -\frac{1}{5} and \frac{4}{3} to get \frac{17}{15}.

$$8x^{4}y^{\frac{17}{15}}$$

Differentiate w.r.t. x

$$32y^{\frac{17}{15}}x^{3}$$