Solve (frac{5xy^{2}}{3x^{-2}y^{-3}})^{3}(3x^-3y^-1/5x^3y^7)

$$( \frac { 5 x y ^ { 2 } } { 3 x ^ { - 2 } y ^ { - 3 } } ) ^ { 3 } ( \frac { 3 x ^ { - 3 } y ^ { - 1 } } { 5 x ^ { 3 } y ^ { 7 } } )$$

Evaluate

$$\frac{25x^{3}y^{7}}{9}$$

Solution Steps

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

$$\left(\frac{5x^{3}y^{5}}{3}\right)^{3}\times \frac{3x^{-3}y^{-1}}{5x^{3}y^{7}}$$

To raise \frac{5x^{3}y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x^{3}y^{5}\right)^{3}}{3^{3}}\times \frac{3x^{-3}y^{-1}}{5x^{3}y^{7}}$$

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

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

Multiply \frac{\left(5x^{3}y^{5}\right)^{3}}{3^{3}} times \frac{3}{5x^{6}y^{8}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$\frac{\left(5x^{3}y^{5}\right)^{3}}{5\times 3^{2}x^{6}y^{8}}$$

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

$$\frac{5^{3}\left(x^{3}\right)^{3}\left(y^{5}\right)^{3}}{5\times 3^{2}x^{6}y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{5^{3}x^{9}\left(y^{5}\right)^{3}}{5\times 3^{2}x^{6}y^{8}}$$

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

$$\frac{5^{3}x^{9}y^{15}}{5\times 3^{2}x^{6}y^{8}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125x^{9}y^{15}}{5\times 3^{2}x^{6}y^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{125x^{9}y^{15}}{5\times 9x^{6}y^{8}}$$

Multiply 5 and 9 to get 45.

$$\frac{125x^{9}y^{15}}{45x^{6}y^{8}}$$

Cancel out 5x^{6}y^{8} in both numerator and denominator.

$$\frac{25x^{3}y^{7}}{9}$$

Expand

$$\frac{25x^{3}y^{7}}{9}$$

Solution Steps

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

$$\left(\frac{5x^{3}y^{5}}{3}\right)^{3}\times \frac{3x^{-3}y^{-1}}{5x^{3}y^{7}}$$

To raise \frac{5x^{3}y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x^{3}y^{5}\right)^{3}}{3^{3}}\times \frac{3x^{-3}y^{-1}}{5x^{3}y^{7}}$$

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

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

Multiply \frac{\left(5x^{3}y^{5}\right)^{3}}{3^{3}} times \frac{3}{5x^{6}y^{8}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$\frac{\left(5x^{3}y^{5}\right)^{3}}{5\times 3^{2}x^{6}y^{8}}$$

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

$$\frac{5^{3}\left(x^{3}\right)^{3}\left(y^{5}\right)^{3}}{5\times 3^{2}x^{6}y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{5^{3}x^{9}\left(y^{5}\right)^{3}}{5\times 3^{2}x^{6}y^{8}}$$

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

$$\frac{5^{3}x^{9}y^{15}}{5\times 3^{2}x^{6}y^{8}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125x^{9}y^{15}}{5\times 3^{2}x^{6}y^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{125x^{9}y^{15}}{5\times 9x^{6}y^{8}}$$

Multiply 5 and 9 to get 45.

$$\frac{125x^{9}y^{15}}{45x^{6}y^{8}}$$

Cancel out 5x^{6}y^{8} in both numerator and denominator.

$$\frac{25x^{3}y^{7}}{9}$$