Solve (frac{3x^{3}y^{0}}{x^{-2}})^{4}*(y^2x^-4/5xy^-8)^3

$$( \frac { 3 x ^ { 3 } y ^ { 0 } } { x ^ { - 2 } } ) ^ { 4 } \cdot ( \frac { y ^ { 2 } x ^ { - 4 } } { 5 x y ^ { - 8 } } ) ^ { 3 }$$

Evaluate

$$\frac{81x^{5}y^{30}}{125}$$

Solution Steps

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

$$\left(3y^{0}x^{5}\right)^{4}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Expand \left(3y^{0}x^{5}\right)^{4}.

$$3^{4}\left(y^{0}\right)^{4}\left(x^{5}\right)^{4}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 0 and 4 to get 0.

$$3^{4}y^{0}\left(x^{5}\right)^{4}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$3^{4}y^{0}x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Calculate 3 to the power of 4 and get 81.

$$81y^{0}x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Calculate y to the power of 0 and get 1.

$$81\times 1x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Multiply 81 and 1 to get 81.

$$81x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

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

$$81x^{20}\times \left(\frac{x^{-4}y^{10}}{5x}\right)^{3}$$

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

$$81x^{20}\times \left(\frac{y^{10}}{5x^{5}}\right)^{3}$$

To raise \frac{y^{10}}{5x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$81x^{20}\times \frac{\left(y^{10}\right)^{3}}{\left(5x^{5}\right)^{3}}$$

Express 81\times \frac{\left(y^{10}\right)^{3}}{\left(5x^{5}\right)^{3}} as a single fraction.

$$\frac{81\left(y^{10}\right)^{3}}{\left(5x^{5}\right)^{3}}x^{20}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

$$\frac{81y^{30}}{\left(5x^{5}\right)^{3}}x^{20}$$

Expand \left(5x^{5}\right)^{3}.

$$\frac{81y^{30}}{5^{3}\left(x^{5}\right)^{3}}x^{20}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{81y^{30}}{5^{3}x^{15}}x^{20}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{81y^{30}}{125x^{15}}x^{20}$$

Express \frac{81y^{30}}{125x^{15}}x^{20} as a single fraction.

$$\frac{81y^{30}x^{20}}{125x^{15}}$$

Cancel out x^{15} in both numerator and denominator.

$$\frac{81x^{5}y^{30}}{125}$$

Expand

$$\frac{81x^{5}y^{30}}{125}$$

Solution Steps

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

$$\left(3y^{0}x^{5}\right)^{4}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Expand \left(3y^{0}x^{5}\right)^{4}.

$$3^{4}\left(y^{0}\right)^{4}\left(x^{5}\right)^{4}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 0 and 4 to get 0.

$$3^{4}y^{0}\left(x^{5}\right)^{4}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$3^{4}y^{0}x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Calculate 3 to the power of 4 and get 81.

$$81y^{0}x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Calculate y to the power of 0 and get 1.

$$81\times 1x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

Multiply 81 and 1 to get 81.

$$81x^{20}\times \left(\frac{y^{2}x^{-4}}{5xy^{-8}}\right)^{3}$$

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

$$81x^{20}\times \left(\frac{x^{-4}y^{10}}{5x}\right)^{3}$$

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

$$81x^{20}\times \left(\frac{y^{10}}{5x^{5}}\right)^{3}$$

To raise \frac{y^{10}}{5x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$81x^{20}\times \frac{\left(y^{10}\right)^{3}}{\left(5x^{5}\right)^{3}}$$

Express 81\times \frac{\left(y^{10}\right)^{3}}{\left(5x^{5}\right)^{3}} as a single fraction.

$$\frac{81\left(y^{10}\right)^{3}}{\left(5x^{5}\right)^{3}}x^{20}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

$$\frac{81y^{30}}{\left(5x^{5}\right)^{3}}x^{20}$$

Expand \left(5x^{5}\right)^{3}.

$$\frac{81y^{30}}{5^{3}\left(x^{5}\right)^{3}}x^{20}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{81y^{30}}{5^{3}x^{15}}x^{20}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{81y^{30}}{125x^{15}}x^{20}$$

Express \frac{81y^{30}}{125x^{15}}x^{20} as a single fraction.

$$\frac{81y^{30}x^{20}}{125x^{15}}$$

Cancel out x^{15} in both numerator and denominator.

$$\frac{81x^{5}y^{30}}{125}$$