Solve (9x^3y^2)^-2/18xy^-3

$$\frac { ( 9 x ^ { 3 } y ^ { 2 } ) ^ { - 2 } } { 18 x y ^ { - 3 } }$$

Evaluate

$$\frac{1}{1458yx^{7}}$$

Solution Steps

Expand \left(9x^{3}y^{2}\right)^{-2}.

$$\frac{9^{-2}\left(x^{3}\right)^{-2}\left(y^{2}\right)^{-2}}{18xy^{-3}}$$

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

$$\frac{9^{-2}x^{-6}\left(y^{2}\right)^{-2}}{18xy^{-3}}$$

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

$$\frac{9^{-2}x^{-6}y^{-4}}{18xy^{-3}}$$

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

$$\frac{\frac{1}{81}x^{-6}y^{-4}}{18xy^{-3}}$$

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

$$\frac{\frac{1}{81}}{18y^{1}x^{7}}$$

Calculate y to the power of 1 and get y.

$$\frac{\frac{1}{81}}{18yx^{7}}$$

Express \frac{\frac{1}{81}}{18yx^{7}} as a single fraction.

$$\frac{1}{81\times 18yx^{7}}$$

Multiply 81 and 18 to get 1458.

$$\frac{1}{1458yx^{7}}$$

Expand

$$\frac{1}{1458yx^{7}}$$

Solution Steps

Expand \left(9x^{3}y^{2}\right)^{-2}.

$$\frac{9^{-2}\left(x^{3}\right)^{-2}\left(y^{2}\right)^{-2}}{18xy^{-3}}$$

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

$$\frac{9^{-2}x^{-6}\left(y^{2}\right)^{-2}}{18xy^{-3}}$$

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

$$\frac{9^{-2}x^{-6}y^{-4}}{18xy^{-3}}$$

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

$$\frac{\frac{1}{81}x^{-6}y^{-4}}{18xy^{-3}}$$

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

$$\frac{\frac{1}{81}}{18y^{1}x^{7}}$$

Calculate y to the power of 1 and get y.

$$\frac{\frac{1}{81}}{18yx^{7}}$$

Express \frac{\frac{1}{81}}{18yx^{7}} as a single fraction.

$$\frac{1}{81\times 18yx^{7}}$$

Multiply 81 and 18 to get 1458.

$$\frac{1}{1458yx^{7}}$$