Solve frac{12x^{8}y^-7}{(4x^-2y^-6)^2}

$$\frac { 12 x ^ { 8 } y ^ { - 7 } } { ( 4 x ^ { - 2 } y ^ { - 6 } ) ^ { 2 } }$$

Evaluate

$$\frac{3y^{5}x^{12}}{4}$$

Solution Steps

Expand \left(4x^{-2}y^{-6}\right)^{2}.

$$\frac{12x^{8}y^{-7}}{4^{2}\left(x^{-2}\right)^{2}\left(y^{-6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{12x^{8}y^{-7}}{4^{2}x^{-4}\left(y^{-6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and 2 to get -12.

$$\frac{12x^{8}y^{-7}}{4^{2}x^{-4}y^{-12}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{12x^{8}y^{-7}}{16x^{-4}y^{-12}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3y^{-7}x^{8}}{4y^{-12}x^{-4}}$$

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

$$\frac{3y^{5}x^{12}}{4}$$

Expand

$$\frac{3y^{5}x^{12}}{4}$$

Solution Steps

Expand \left(4x^{-2}y^{-6}\right)^{2}.

$$\frac{12x^{8}y^{-7}}{4^{2}\left(x^{-2}\right)^{2}\left(y^{-6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{12x^{8}y^{-7}}{4^{2}x^{-4}\left(y^{-6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and 2 to get -12.

$$\frac{12x^{8}y^{-7}}{4^{2}x^{-4}y^{-12}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{12x^{8}y^{-7}}{16x^{-4}y^{-12}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3y^{-7}x^{8}}{4y^{-12}x^{-4}}$$

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

$$\frac{3y^{5}x^{12}}{4}$$