Solve (32x^35y^15)^-frac{4{5}}

$$( 32 x ^ { 35 } y ^ { 15 } ) ^ { - \frac { 4 } { 5 } }$$

Evaluate

$$\frac{1}{16y^{12}x^{28}}$$

Solution Steps

Expand \left(32x^{35}y^{15}\right)^{-\frac{4}{5}}.

$$32^{-\frac{4}{5}}\left(x^{35}\right)^{-\frac{4}{5}}\left(y^{15}\right)^{-\frac{4}{5}}$$

To raise a power to another power, multiply the exponents. Multiply 35 and -\frac{4}{5} to get -28.

$$32^{-\frac{4}{5}}x^{-28}\left(y^{15}\right)^{-\frac{4}{5}}$$

To raise a power to another power, multiply the exponents. Multiply 15 and -\frac{4}{5} to get -12.

$$32^{-\frac{4}{5}}x^{-28}y^{-12}$$

Calculate 32 to the power of -\frac{4}{5} and get \frac{1}{16}.

$$\frac{1}{16}x^{-28}y^{-12}$$

Differentiate w.r.t. x

$$-\frac{7}{4y^{12}x^{29}}$$