Solve {left(2x^4{y}^frac{-4{5}}right)}^4y4/3

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

Evaluate

$$\frac{64x^{16}}{3y^{\frac{11}{5}}}$$

Solution Steps

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

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

Expand \left(2x^{4}y^{-\frac{4}{5}}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$2^{4}x^{16}\left(y^{-\frac{4}{5}}\right)^{4}y\times \frac{4}{3}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{4}{5} and 4 to get -\frac{16}{5}.

$$2^{4}x^{16}y^{-\frac{16}{5}}y\times \frac{4}{3}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{16}y^{-\frac{16}{5}}y\times \frac{4}{3}$$

To multiply powers of the same base, add their exponents. Add -\frac{16}{5} and 1 to get -\frac{11}{5}.

$$16x^{16}y^{-\frac{11}{5}}\times \frac{4}{3}$$

Multiply 16 and \frac{4}{3} to get \frac{64}{3}.

$$\frac{64}{3}x^{16}y^{-\frac{11}{5}}$$

Expand

$$\frac{64x^{16}}{3y^{\frac{11}{5}}}$$

Solution Steps

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

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

Expand \left(2x^{4}y^{-\frac{4}{5}}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$2^{4}x^{16}\left(y^{-\frac{4}{5}}\right)^{4}y\times \frac{4}{3}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{4}{5} and 4 to get -\frac{16}{5}.

$$2^{4}x^{16}y^{-\frac{16}{5}}y\times \frac{4}{3}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{16}y^{-\frac{16}{5}}y\times \frac{4}{3}$$

To multiply powers of the same base, add their exponents. Add -\frac{16}{5} and 1 to get -\frac{11}{5}.

$$16x^{16}y^{-\frac{11}{5}}\times \frac{4}{3}$$

Multiply 16 and \frac{4}{3} to get \frac{64}{3}.

$$\frac{64}{3}x^{16}y^{-\frac{11}{5}}$$