Solve [(3x^{2}y^{-2})^{0}(3x^2y^-2)^-2]^-2

$$[ ( 3 x ^ { 2 } y ^ { - 2 } ) ^ { 0 } ( 3 x ^ { 2 } y ^ { - 2 } ) ^ { - 2 } ] ^ { - 2 }$$

Evaluate

$$81\times \left(\frac{x}{y}\right)^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and -2 to get -2.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate \frac{1}{9} to the power of -2 and get 81.

$$81x^{8}y^{-8}$$

Expand

$$81\times \left(\frac{x}{y}\right)^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and -2 to get -2.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate \frac{1}{9} to the power of -2 and get 81.

$$81x^{8}y^{-8}$$