Solve frac{(10x^{-2}y)^3}{(50x^3y^-1)^2}

$$\frac { ( 10 x ^ { - 2 } y ) ^ { 3 } } { ( 50 x ^ { 3 } y ^ { - 1 } ) ^ { 2 } }$$

Evaluate

$$\frac{2y^{5}}{5x^{12}}$$

Solution Steps

Expand \left(10x^{-2}y\right)^{3}.

$$\frac{10^{3}\left(x^{-2}\right)^{3}y^{3}}{\left(50x^{3}y^{-1}\right)^{2}}$$

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

$$\frac{10^{3}x^{-6}y^{3}}{\left(50x^{3}y^{-1}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{1000x^{-6}y^{3}}{\left(50x^{3}y^{-1}\right)^{2}}$$

Expand \left(50x^{3}y^{-1}\right)^{2}.

$$\frac{1000x^{-6}y^{3}}{50^{2}\left(x^{3}\right)^{2}\left(y^{-1}\right)^{2}}$$

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

$$\frac{1000x^{-6}y^{3}}{50^{2}x^{6}\left(y^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{1000x^{-6}y^{3}}{50^{2}x^{6}y^{-2}}$$

Calculate 50 to the power of 2 and get 2500.

$$\frac{1000x^{-6}y^{3}}{2500x^{6}y^{-2}}$$

Cancel out 500 in both numerator and denominator.

$$\frac{2x^{-6}y^{3}}{5y^{-2}x^{6}}$$

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

$$\frac{2x^{-6}y^{5}}{5x^{6}}$$

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

$$\frac{2y^{5}}{5x^{12}}$$

Expand

$$\frac{2y^{5}}{5x^{12}}$$

Solution Steps

Expand \left(10x^{-2}y\right)^{3}.

$$\frac{10^{3}\left(x^{-2}\right)^{3}y^{3}}{\left(50x^{3}y^{-1}\right)^{2}}$$

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

$$\frac{10^{3}x^{-6}y^{3}}{\left(50x^{3}y^{-1}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{1000x^{-6}y^{3}}{\left(50x^{3}y^{-1}\right)^{2}}$$

Expand \left(50x^{3}y^{-1}\right)^{2}.

$$\frac{1000x^{-6}y^{3}}{50^{2}\left(x^{3}\right)^{2}\left(y^{-1}\right)^{2}}$$

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

$$\frac{1000x^{-6}y^{3}}{50^{2}x^{6}\left(y^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{1000x^{-6}y^{3}}{50^{2}x^{6}y^{-2}}$$

Calculate 50 to the power of 2 and get 2500.

$$\frac{1000x^{-6}y^{3}}{2500x^{6}y^{-2}}$$

Cancel out 500 in both numerator and denominator.

$$\frac{2x^{-6}y^{3}}{5y^{-2}x^{6}}$$

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

$$\frac{2x^{-6}y^{5}}{5x^{6}}$$

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

$$\frac{2y^{5}}{5x^{12}}$$