Solve frac{(9x^{-2}y^{0}z^{2})^{-2}(x^{2}z^{-2})^{2}}{(3x^3y^-3z^-1)^4}=

$$\frac { ( 9 x ^ { - 2 } y ^ { 0 } z ^ { 2 } ) ^ { - 2 } ( x ^ { 2 } z ^ { - 2 } ) ^ { 2 } } { ( 3 x ^ { 3 } y ^ { - 3 } z ^ { - 1 } ) ^ { 4 } } =$$

Evaluate

$$\frac{y^{12}}{6561\left(xz\right)^{4}}$$

Solution Steps

Calculate y to the power of 0 and get 1.

$$\frac{\left(9x^{-2}\times 1z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

Multiply 9 and 1 to get 9.

$$\frac{\left(9x^{-2}z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

Expand \left(9x^{-2}z^{2}\right)^{-2}.

$$\frac{9^{-2}\left(x^{-2}\right)^{-2}\left(z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{9^{-2}x^{4}\left(z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{9^{-2}x^{4}z^{-4}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}\left(x^{2}\right)^{2}\left(z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}x^{4}\left(z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}x^{4}z^{-4}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\frac{1}{81}x^{8}z^{-4}z^{-4}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add -4 and -4 to get -8.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

Expand \left(3x^{3}y^{-3}z^{-1}\right)^{4}.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}\left(x^{3}\right)^{4}\left(y^{-3}\right)^{4}\left(z^{-1}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}x^{12}\left(y^{-3}\right)^{4}\left(z^{-1}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}x^{12}y^{-12}\left(z^{-1}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}x^{12}y^{-12}z^{-4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{81x^{12}y^{-12}z^{-4}}$$

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

$$\frac{\frac{1}{81}z^{-8}}{81y^{-12}z^{-4}x^{4}}$$

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

$$\frac{\frac{1}{81}}{81y^{-12}x^{4}z^{4}}$$

Express \frac{\frac{1}{81}}{81y^{-12}x^{4}z^{4}} as a single fraction.

$$\frac{1}{81\times 81y^{-12}x^{4}z^{4}}$$

Multiply 81 and 81 to get 6561.

$$\frac{1}{6561y^{-12}x^{4}z^{4}}$$

Expand

$$\frac{y^{12}}{6561\left(xz\right)^{4}}$$

Solution Steps

Calculate y to the power of 0 and get 1.

$$\frac{\left(9x^{-2}\times 1z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

Multiply 9 and 1 to get 9.

$$\frac{\left(9x^{-2}z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

Expand \left(9x^{-2}z^{2}\right)^{-2}.

$$\frac{9^{-2}\left(x^{-2}\right)^{-2}\left(z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{9^{-2}x^{4}\left(z^{2}\right)^{-2}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{9^{-2}x^{4}z^{-4}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}\left(x^{2}z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}\left(x^{2}\right)^{2}\left(z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}x^{4}\left(z^{-2}\right)^{2}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

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

$$\frac{\frac{1}{81}x^{4}z^{-4}x^{4}z^{-4}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\frac{1}{81}x^{8}z^{-4}z^{-4}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add -4 and -4 to get -8.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{\left(3x^{3}y^{-3}z^{-1}\right)^{4}}$$

Expand \left(3x^{3}y^{-3}z^{-1}\right)^{4}.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}\left(x^{3}\right)^{4}\left(y^{-3}\right)^{4}\left(z^{-1}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}x^{12}\left(y^{-3}\right)^{4}\left(z^{-1}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}x^{12}y^{-12}\left(z^{-1}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{3^{4}x^{12}y^{-12}z^{-4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{1}{81}x^{8}z^{-8}}{81x^{12}y^{-12}z^{-4}}$$

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

$$\frac{\frac{1}{81}z^{-8}}{81y^{-12}z^{-4}x^{4}}$$

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

$$\frac{\frac{1}{81}}{81y^{-12}x^{4}z^{4}}$$

Express \frac{\frac{1}{81}}{81y^{-12}x^{4}z^{4}} as a single fraction.

$$\frac{1}{81\times 81y^{-12}x^{4}z^{4}}$$

Multiply 81 and 81 to get 6561.

$$\frac{1}{6561y^{-12}x^{4}z^{4}}$$