Solve (frac{7x^{-3}y^{2}}{3x^{2}y})^{5}(9xy^-4/49x^-5y^3)^2

$$( \frac { 7 x ^ { - 3 } y ^ { 2 } } { 3 x ^ { 2 } y } ) ^ { 5 } ( \frac { 9 x y ^ { - 4 } } { 49 x ^ { - 5 } y ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{7}{3y^{9}x^{13}}$$

Solution Steps

Cancel out y in both numerator and denominator.

$$\left(\frac{7x^{-3}y}{3x^{2}}\right)^{5}\times \left(\frac{9xy^{-4}}{49x^{-5}y^{3}}\right)^{2}$$

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

$$\left(\frac{7y}{3x^{5}}\right)^{5}\times \left(\frac{9xy^{-4}}{49x^{-5}y^{3}}\right)^{2}$$

To raise \frac{7y}{3x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \left(\frac{9xy^{-4}}{49x^{-5}y^{3}}\right)^{2}$$

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

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \left(\frac{9y^{-4}x^{6}}{49y^{3}}\right)^{2}$$

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

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \left(\frac{9x^{6}}{49y^{7}}\right)^{2}$$

To raise \frac{9x^{6}}{49y^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \frac{\left(9x^{6}\right)^{2}}{\left(49y^{7}\right)^{2}}$$

Multiply \frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}} times \frac{\left(9x^{6}\right)^{2}}{\left(49y^{7}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(7y\right)^{5}\times \left(9x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Expand \left(7y\right)^{5}.

$$\frac{7^{5}y^{5}\times \left(9x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Calculate 7 to the power of 5 and get 16807.

$$\frac{16807y^{5}\times \left(9x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Expand \left(9x^{6}\right)^{2}.

$$\frac{16807y^{5}\times 9^{2}\left(x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{16807y^{5}\times 9^{2}x^{12}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{16807y^{5}\times 81x^{12}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Multiply 16807 and 81 to get 1361367.

$$\frac{1361367y^{5}x^{12}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

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

$$\frac{1361367y^{5}x^{12}}{3^{5}\left(x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{1361367y^{5}x^{12}}{3^{5}x^{25}\times \left(49y^{7}\right)^{2}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times \left(49y^{7}\right)^{2}}$$

Expand \left(49y^{7}\right)^{2}.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times 49^{2}\left(y^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times 49^{2}y^{14}}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times 2401y^{14}}$$

Multiply 243 and 2401 to get 583443.

$$\frac{1361367y^{5}x^{12}}{583443x^{25}y^{14}}$$

Cancel out 194481y^{5}x^{12} in both numerator and denominator.

$$\frac{7}{3y^{9}x^{13}}$$

Expand

$$\frac{7}{3y^{9}x^{13}}$$

Solution Steps

Cancel out y in both numerator and denominator.

$$\left(\frac{7x^{-3}y}{3x^{2}}\right)^{5}\times \left(\frac{9xy^{-4}}{49x^{-5}y^{3}}\right)^{2}$$

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

$$\left(\frac{7y}{3x^{5}}\right)^{5}\times \left(\frac{9xy^{-4}}{49x^{-5}y^{3}}\right)^{2}$$

To raise \frac{7y}{3x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \left(\frac{9xy^{-4}}{49x^{-5}y^{3}}\right)^{2}$$

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

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \left(\frac{9y^{-4}x^{6}}{49y^{3}}\right)^{2}$$

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

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \left(\frac{9x^{6}}{49y^{7}}\right)^{2}$$

To raise \frac{9x^{6}}{49y^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}}\times \frac{\left(9x^{6}\right)^{2}}{\left(49y^{7}\right)^{2}}$$

Multiply \frac{\left(7y\right)^{5}}{\left(3x^{5}\right)^{5}} times \frac{\left(9x^{6}\right)^{2}}{\left(49y^{7}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(7y\right)^{5}\times \left(9x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Expand \left(7y\right)^{5}.

$$\frac{7^{5}y^{5}\times \left(9x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Calculate 7 to the power of 5 and get 16807.

$$\frac{16807y^{5}\times \left(9x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Expand \left(9x^{6}\right)^{2}.

$$\frac{16807y^{5}\times 9^{2}\left(x^{6}\right)^{2}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{16807y^{5}\times 9^{2}x^{12}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{16807y^{5}\times 81x^{12}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

Multiply 16807 and 81 to get 1361367.

$$\frac{1361367y^{5}x^{12}}{\left(3x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

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

$$\frac{1361367y^{5}x^{12}}{3^{5}\left(x^{5}\right)^{5}\times \left(49y^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{1361367y^{5}x^{12}}{3^{5}x^{25}\times \left(49y^{7}\right)^{2}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times \left(49y^{7}\right)^{2}}$$

Expand \left(49y^{7}\right)^{2}.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times 49^{2}\left(y^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times 49^{2}y^{14}}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{1361367y^{5}x^{12}}{243x^{25}\times 2401y^{14}}$$

Multiply 243 and 2401 to get 583443.

$$\frac{1361367y^{5}x^{12}}{583443x^{25}y^{14}}$$

Cancel out 194481y^{5}x^{12} in both numerator and denominator.

$$\frac{7}{3y^{9}x^{13}}$$