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

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

Evaluate

$$\frac{y^{10}x^{16}}{27}$$

Solution Steps

Expand \left(3x^{-5}y^{-2}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply -5 and -2 to get 10.

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

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

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

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{10}y^{4}}{3x^{-6}y^{-6}}$$

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

$$\frac{\frac{1}{9}y^{10}x^{16}}{3}$$

Divide \frac{1}{9}y^{10}x^{16} by 3 to get \frac{1}{27}y^{10}x^{16}.

$$\frac{1}{27}y^{10}x^{16}$$

Expand

$$\frac{y^{10}x^{16}}{27}$$

Solution Steps

Expand \left(3x^{-5}y^{-2}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply -5 and -2 to get 10.

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

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

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

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{10}y^{4}}{3x^{-6}y^{-6}}$$

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

$$\frac{\frac{1}{9}y^{10}x^{16}}{3}$$

Divide \frac{1}{9}y^{10}x^{16} by 3 to get \frac{1}{27}y^{10}x^{16}.

$$\frac{1}{27}y^{10}x^{16}$$