Solve frac{(2x^{-3}y^{-1})^3}{(y^2x^-2)^2}

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

Evaluate

$$\frac{8}{x^{5}y^{7}}$$

Solution Steps

Expand \left(2x^{-3}y^{-1}\right)^{3}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{-9}y^{-3}}{\left(y^{2}x^{-2}\right)^{2}}$$

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

$$\frac{8x^{-9}y^{-3}}{\left(y^{2}\right)^{2}\left(x^{-2}\right)^{2}}$$

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

$$\frac{8x^{-9}y^{-3}}{y^{4}\left(x^{-2}\right)^{2}}$$

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

$$\frac{8x^{-9}y^{-3}}{y^{4}x^{-4}}$$

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

$$\frac{8}{x^{5}y^{7}}$$

Expand

$$\frac{8}{x^{5}y^{7}}$$

Solution Steps

Expand \left(2x^{-3}y^{-1}\right)^{3}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{-9}y^{-3}}{\left(y^{2}x^{-2}\right)^{2}}$$

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

$$\frac{8x^{-9}y^{-3}}{\left(y^{2}\right)^{2}\left(x^{-2}\right)^{2}}$$

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

$$\frac{8x^{-9}y^{-3}}{y^{4}\left(x^{-2}\right)^{2}}$$

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

$$\frac{8x^{-9}y^{-3}}{y^{4}x^{-4}}$$

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

$$\frac{8}{x^{5}y^{7}}$$