Solve frac{(2x^{3}y^-4)^-2}{10x^-3y^4}

$$\frac { ( 2 x ^ { 3 } y ^ { - 4 } ) ^ { - 2 } } { 10 x ^ { - 3 } y ^ { 4 } }$$

Evaluate

$$\frac{y^{4}}{40x^{3}}$$

Solution Steps

Expand \left(2x^{3}y^{-4}\right)^{-2}.

$$\frac{2^{-2}\left(x^{3}\right)^{-2}\left(y^{-4}\right)^{-2}}{10x^{-3}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{2^{-2}x^{-6}\left(y^{-4}\right)^{-2}}{10x^{-3}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$\frac{2^{-2}x^{-6}y^{8}}{10x^{-3}y^{4}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}x^{-6}y^{8}}{10x^{-3}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{\frac{1}{4}x^{-6}y^{4}}{10x^{-3}}$$

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

$$\frac{\frac{1}{4}y^{4}}{10x^{3}}$$

Expand

$$\frac{y^{4}}{40x^{3}}$$

Solution Steps

Expand \left(2x^{3}y^{-4}\right)^{-2}.

$$\frac{2^{-2}\left(x^{3}\right)^{-2}\left(y^{-4}\right)^{-2}}{10x^{-3}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{2^{-2}x^{-6}\left(y^{-4}\right)^{-2}}{10x^{-3}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$\frac{2^{-2}x^{-6}y^{8}}{10x^{-3}y^{4}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}x^{-6}y^{8}}{10x^{-3}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{\frac{1}{4}x^{-6}y^{4}}{10x^{-3}}$$

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

$$\frac{\frac{1}{4}y^{4}}{10x^{3}}$$