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

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

Evaluate

$$2x^{5}y^{13}$$

Solution Steps

Cancel out x in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$8x^{2}y^{4}\times \left(\frac{4}{x^{3}y^{9}}\right)^{-1}$$

To raise \frac{4}{x^{3}y^{9}} to a power, raise both numerator and denominator to the power and then divide.

$$8x^{2}y^{4}\times \frac{4^{-1}}{\left(x^{3}y^{9}\right)^{-1}}$$

Express 8\times \frac{4^{-1}}{\left(x^{3}y^{9}\right)^{-1}} as a single fraction.

$$\frac{8\times 4^{-1}}{\left(x^{3}y^{9}\right)^{-1}}x^{2}y^{4}$$

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

$$\frac{8\times \frac{1}{4}}{\left(x^{3}y^{9}\right)^{-1}}x^{2}y^{4}$$

Multiply 8 and \frac{1}{4} to get 2.

$$\frac{2}{\left(x^{3}y^{9}\right)^{-1}}x^{2}y^{4}$$

Expand \left(x^{3}y^{9}\right)^{-1}.

$$\frac{2}{\left(x^{3}\right)^{-1}\left(y^{9}\right)^{-1}}x^{2}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{2}{x^{-3}\left(y^{9}\right)^{-1}}x^{2}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 9 and -1 to get -9.

$$\frac{2}{x^{-3}y^{-9}}x^{2}y^{4}$$

Express \frac{2}{x^{-3}y^{-9}}x^{2} as a single fraction.

$$\frac{2x^{2}}{x^{-3}y^{-9}}y^{4}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{2x^{5}}{y^{-9}}y^{4}$$

Express \frac{2x^{5}}{y^{-9}}y^{4} as a single fraction.

$$\frac{2x^{5}y^{4}}{y^{-9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$2x^{5}y^{13}$$

Differentiate w.r.t. x

$$10x^{4}y^{13}$$