Solve frac{(3x^{3}y^-9)^-2}{9x^-2y^-9}

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

Evaluate

$$\frac{y^{27}}{81x^{4}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply -9 and -2 to get 18.

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

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

$$\frac{\frac{1}{9}x^{-6}y^{18}}{9x^{-2}y^{-9}}$$

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

$$\frac{\frac{1}{9}x^{-6}y^{27}}{9x^{-2}}$$

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

$$\frac{\frac{1}{9}y^{27}}{9x^{4}}$$

Expand

$$\frac{y^{27}}{81x^{4}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply -9 and -2 to get 18.

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

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

$$\frac{\frac{1}{9}x^{-6}y^{18}}{9x^{-2}y^{-9}}$$

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

$$\frac{\frac{1}{9}x^{-6}y^{27}}{9x^{-2}}$$

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

$$\frac{\frac{1}{9}y^{27}}{9x^{4}}$$