Solve left(5xyright)^-83x^-2y/left(x^3right)^4{y^-2}

$$\frac{ { \left(5xy \right) }^{ -8 } 3 { x }^{ -2 } y }{ { \left( { x }^{ 3 } \right) }^{ 4 } { y }^{ -2 } }$$

Evaluate

$$\frac{3}{390625y^{5}x^{22}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(5xy\right)^{-8}\times 3x^{-2}y}{x^{12}y^{-2}}$$

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

$$\frac{3\times \left(5xy\right)^{-8}x^{-2}y^{3}}{x^{12}}$$

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

$$\frac{3\times \left(5xy\right)^{-8}y^{3}}{x^{14}}$$

Expand \left(5xy\right)^{-8}.

$$\frac{3\times 5^{-8}x^{-8}y^{-8}y^{3}}{x^{14}}$$

Calculate 5 to the power of -8 and get \frac{1}{390625}.

$$\frac{3\times \frac{1}{390625}x^{-8}y^{-8}y^{3}}{x^{14}}$$

Multiply 3 and \frac{1}{390625} to get \frac{3}{390625}.

$$\frac{\frac{3}{390625}x^{-8}y^{-8}y^{3}}{x^{14}}$$

To multiply powers of the same base, add their exponents. Add -8 and 3 to get -5.

$$\frac{\frac{3}{390625}x^{-8}y^{-5}}{x^{14}}$$

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

$$\frac{\frac{3}{390625}y^{-5}}{x^{22}}$$

Expand

$$\frac{3}{390625y^{5}x^{22}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(5xy\right)^{-8}\times 3x^{-2}y}{x^{12}y^{-2}}$$

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

$$\frac{3\times \left(5xy\right)^{-8}x^{-2}y^{3}}{x^{12}}$$

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

$$\frac{3\times \left(5xy\right)^{-8}y^{3}}{x^{14}}$$

Expand \left(5xy\right)^{-8}.

$$\frac{3\times 5^{-8}x^{-8}y^{-8}y^{3}}{x^{14}}$$

Calculate 5 to the power of -8 and get \frac{1}{390625}.

$$\frac{3\times \frac{1}{390625}x^{-8}y^{-8}y^{3}}{x^{14}}$$

Multiply 3 and \frac{1}{390625} to get \frac{3}{390625}.

$$\frac{\frac{3}{390625}x^{-8}y^{-8}y^{3}}{x^{14}}$$

To multiply powers of the same base, add their exponents. Add -8 and 3 to get -5.

$$\frac{\frac{3}{390625}x^{-8}y^{-5}}{x^{14}}$$

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

$$\frac{\frac{3}{390625}y^{-5}}{x^{22}}$$