Solve x^3/x^5y^-2(2xy)^5

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

Evaluate

$$32x^{3}y^{7}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\frac{1}{y^{-2}x^{2}}\times \left(2xy\right)^{5}$$

Expand \left(2xy\right)^{5}.

$$\frac{1}{y^{-2}x^{2}}\times 2^{5}x^{5}y^{5}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1}{y^{-2}x^{2}}\times 32x^{5}y^{5}$$

Express \frac{1}{y^{-2}x^{2}}\times 32 as a single fraction.

$$\frac{32}{y^{-2}x^{2}}x^{5}y^{5}$$

Express \frac{32}{y^{-2}x^{2}}x^{5} as a single fraction.

$$\frac{32x^{5}}{y^{-2}x^{2}}y^{5}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{32x^{3}}{y^{-2}}y^{5}$$

Express \frac{32x^{3}}{y^{-2}}y^{5} as a single fraction.

$$\frac{32x^{3}y^{5}}{y^{-2}}$$

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

$$32x^{3}y^{7}$$

Expand

$$32x^{3}y^{7}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\frac{1}{y^{-2}x^{2}}\times \left(2xy\right)^{5}$$

Expand \left(2xy\right)^{5}.

$$\frac{1}{y^{-2}x^{2}}\times 2^{5}x^{5}y^{5}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1}{y^{-2}x^{2}}\times 32x^{5}y^{5}$$

Express \frac{1}{y^{-2}x^{2}}\times 32 as a single fraction.

$$\frac{32}{y^{-2}x^{2}}x^{5}y^{5}$$

Express \frac{32}{y^{-2}x^{2}}x^{5} as a single fraction.

$$\frac{32x^{5}}{y^{-2}x^{2}}y^{5}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{32x^{3}}{y^{-2}}y^{5}$$

Express \frac{32x^{3}}{y^{-2}}y^{5} as a single fraction.

$$\frac{32x^{3}y^{5}}{y^{-2}}$$

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

$$32x^{3}y^{7}$$