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

$$\frac { ( x ^ { 0 } y ^ { - 3 } ) ^ { 3 } } { ( x ^ { - 2 } y ^ { 2 } ) ^ { - 2 } }$$

Evaluate

$$\frac{1}{x^{4}y^{5}}$$

Solution Steps

Calculate x to the power of 0 and get 1.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

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

Calculate 1 to the power of 3 and get 1.

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

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

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

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

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

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

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

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

$$\frac{1}{x^{4}y^{5}}$$

Expand

$$\frac{1}{x^{4}y^{5}}$$

Solution Steps

Calculate x to the power of 0 and get 1.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

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

Calculate 1 to the power of 3 and get 1.

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

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

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

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

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

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

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

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

$$\frac{1}{x^{4}y^{5}}$$