Solve frac{(2)(5xy)^{-8}(3x^-2y)}{(x^-3)^4y^-2}

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

Evaluate

$$\frac{6x^{2}}{390625y^{5}}$$

Solution Steps

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

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

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

$$2\times 3\times \left(5xy\right)^{-8}y^{3}x^{10}$$

Multiply 2 and 3 to get 6.

$$6\times \left(5xy\right)^{-8}y^{3}x^{10}$$

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

$$6\times 5^{-8}x^{-8}y^{-8}y^{3}x^{10}$$

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

$$6\times \frac{1}{390625}x^{-8}y^{-8}y^{3}x^{10}$$

Multiply 6 and \frac{1}{390625} to get \frac{6}{390625}.

$$\frac{6}{390625}x^{-8}y^{-8}y^{3}x^{10}$$

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

$$\frac{6}{390625}x^{-8}y^{-5}x^{10}$$

To multiply powers of the same base, add their exponents. Add -8 and 10 to get 2.

$$\frac{6}{390625}x^{2}y^{-5}$$

Expand

$$\frac{6x^{2}}{390625y^{5}}$$

Solution Steps

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

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

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

$$2\times 3\times \left(5xy\right)^{-8}y^{3}x^{10}$$

Multiply 2 and 3 to get 6.

$$6\times \left(5xy\right)^{-8}y^{3}x^{10}$$

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

$$6\times 5^{-8}x^{-8}y^{-8}y^{3}x^{10}$$

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

$$6\times \frac{1}{390625}x^{-8}y^{-8}y^{3}x^{10}$$

Multiply 6 and \frac{1}{390625} to get \frac{6}{390625}.

$$\frac{6}{390625}x^{-8}y^{-8}y^{3}x^{10}$$

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

$$\frac{6}{390625}x^{-8}y^{-5}x^{10}$$

To multiply powers of the same base, add their exponents. Add -8 and 10 to get 2.

$$\frac{6}{390625}x^{2}y^{-5}$$