Solve (4x^{2}y^7)^-1(7x^4y^8)

$$( 4 x ^ { 2 } y ^ { 7 } ) ^ { - 1 } ( 7 x ^ { 4 } y ^ { 8 } )$$

Evaluate

$$\frac{7yx^{2}}{4}$$

Solution Steps

Expand \left(4x^{2}y^{7}\right)^{-1}.

$$4^{-1}\left(x^{2}\right)^{-1}\left(y^{7}\right)^{-1}\times 7x^{4}y^{8}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$4^{-1}x^{-2}\left(y^{7}\right)^{-1}\times 7x^{4}y^{8}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -1 to get -7.

$$4^{-1}x^{-2}y^{-7}\times 7x^{4}y^{8}$$

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

$$\frac{1}{4}x^{-2}y^{-7}\times 7x^{4}y^{8}$$

Multiply \frac{1}{4} and 7 to get \frac{7}{4}.

$$\frac{7}{4}x^{-2}y^{-7}x^{4}y^{8}$$

To multiply powers of the same base, add their exponents. Add -2 and 4 to get 2.

$$\frac{7}{4}x^{2}y^{-7}y^{8}$$

To multiply powers of the same base, add their exponents. Add -7 and 8 to get 1.

$$\frac{7}{4}x^{2}y^{1}$$

Calculate y to the power of 1 and get y.

$$\frac{7}{4}x^{2}y$$

Differentiate w.r.t. x

$$\frac{7xy}{2}$$