Solve frac{(3x^{4}y^{-6})(x^{5}y^-6)^-3}{4x^2y^2}

$$\frac { ( 3 x ^ { 4 } y ^ { - 6 } ) ( x ^ { 5 } y ^ { - 6 } ) ^ { - 3 } } { 4 x ^ { 2 } y ^ { 2 } }$$

Evaluate

$$\frac{3y^{10}}{4x^{13}}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

$$\frac{3y^{-6}x^{2}\left(y^{-6}x^{5}\right)^{-3}}{4y^{2}}$$

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

$$\frac{3x^{2}\left(y^{-6}x^{5}\right)^{-3}}{4y^{8}}$$

Expand \left(y^{-6}x^{5}\right)^{-3}.

$$\frac{3x^{2}\left(y^{-6}\right)^{-3}\left(x^{5}\right)^{-3}}{4y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -3 to get 18.

$$\frac{3x^{2}y^{18}\left(x^{5}\right)^{-3}}{4y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{3x^{2}y^{18}x^{-15}}{4y^{8}}$$

To multiply powers of the same base, add their exponents. Add 2 and -15 to get -13.

$$\frac{3x^{-13}y^{18}}{4y^{8}}$$

Cancel out y^{8} in both numerator and denominator.

$$\frac{3x^{-13}y^{10}}{4}$$

Expand

$$\frac{3y^{10}}{4x^{13}}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

$$\frac{3y^{-6}x^{2}\left(y^{-6}x^{5}\right)^{-3}}{4y^{2}}$$

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

$$\frac{3x^{2}\left(y^{-6}x^{5}\right)^{-3}}{4y^{8}}$$

Expand \left(y^{-6}x^{5}\right)^{-3}.

$$\frac{3x^{2}\left(y^{-6}\right)^{-3}\left(x^{5}\right)^{-3}}{4y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -3 to get 18.

$$\frac{3x^{2}y^{18}\left(x^{5}\right)^{-3}}{4y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{3x^{2}y^{18}x^{-15}}{4y^{8}}$$

To multiply powers of the same base, add their exponents. Add 2 and -15 to get -13.

$$\frac{3x^{-13}y^{18}}{4y^{8}}$$

Cancel out y^{8} in both numerator and denominator.

$$\frac{3x^{-13}y^{10}}{4}$$