Solve (frac{9s^{3}a^{4}}{7p^{2}})^3(28p^4a/36s^2)^3=

$$( \frac { 9 s ^ { 3 } a ^ { 4 } } { 7 p ^ { 2 } } ) ^ { 3 } ( \frac { 28 p ^ { 4 } a } { 36 s ^ { 2 } } ) ^ { 3 } =$$

Evaluate

$$s^{3}p^{6}a^{15}$$

Solution Steps

To raise \frac{9s^{3}a^{4}}{7p^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}}\times \left(\frac{28p^{4}a}{36s^{2}}\right)^{3}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}}\times \left(\frac{7ap^{4}}{9s^{2}}\right)^{3}$$

To raise \frac{7ap^{4}}{9s^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}}\times \frac{\left(7ap^{4}\right)^{3}}{\left(9s^{2}\right)^{3}}$$

Multiply \frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}} times \frac{\left(7ap^{4}\right)^{3}}{\left(9s^{2}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9s^{3}a^{4}\right)^{3}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Expand \left(9s^{3}a^{4}\right)^{3}.

$$\frac{9^{3}\left(s^{3}\right)^{3}\left(a^{4}\right)^{3}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

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

$$\frac{9^{3}s^{9}\left(a^{4}\right)^{3}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

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

$$\frac{9^{3}s^{9}a^{12}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{729s^{9}a^{12}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Expand \left(7ap^{4}\right)^{3}.

$$\frac{729s^{9}a^{12}\times 7^{3}a^{3}\left(p^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

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

$$\frac{729s^{9}a^{12}\times 7^{3}a^{3}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{729s^{9}a^{12}\times 343a^{3}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Multiply 729 and 343 to get 250047.

$$\frac{250047s^{9}a^{12}a^{3}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$\frac{250047s^{9}a^{15}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Expand \left(7p^{2}\right)^{3}.

$$\frac{250047s^{9}a^{15}p^{12}}{7^{3}\left(p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{250047s^{9}a^{15}p^{12}}{7^{3}p^{6}\times \left(9s^{2}\right)^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times \left(9s^{2}\right)^{3}}$$

Expand \left(9s^{2}\right)^{3}.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times 9^{3}\left(s^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times 9^{3}s^{6}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times 729s^{6}}$$

Multiply 343 and 729 to get 250047.

$$\frac{250047s^{9}a^{15}p^{12}}{250047p^{6}s^{6}}$$

Cancel out 250047p^{6}s^{6} in both numerator and denominator.

$$s^{3}p^{6}a^{15}$$

Expand

$$s^{3}p^{6}a^{15}$$

Solution Steps

To raise \frac{9s^{3}a^{4}}{7p^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}}\times \left(\frac{28p^{4}a}{36s^{2}}\right)^{3}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}}\times \left(\frac{7ap^{4}}{9s^{2}}\right)^{3}$$

To raise \frac{7ap^{4}}{9s^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}}\times \frac{\left(7ap^{4}\right)^{3}}{\left(9s^{2}\right)^{3}}$$

Multiply \frac{\left(9s^{3}a^{4}\right)^{3}}{\left(7p^{2}\right)^{3}} times \frac{\left(7ap^{4}\right)^{3}}{\left(9s^{2}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9s^{3}a^{4}\right)^{3}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Expand \left(9s^{3}a^{4}\right)^{3}.

$$\frac{9^{3}\left(s^{3}\right)^{3}\left(a^{4}\right)^{3}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

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

$$\frac{9^{3}s^{9}\left(a^{4}\right)^{3}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

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

$$\frac{9^{3}s^{9}a^{12}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{729s^{9}a^{12}\times \left(7ap^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Expand \left(7ap^{4}\right)^{3}.

$$\frac{729s^{9}a^{12}\times 7^{3}a^{3}\left(p^{4}\right)^{3}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

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

$$\frac{729s^{9}a^{12}\times 7^{3}a^{3}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{729s^{9}a^{12}\times 343a^{3}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Multiply 729 and 343 to get 250047.

$$\frac{250047s^{9}a^{12}a^{3}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$\frac{250047s^{9}a^{15}p^{12}}{\left(7p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

Expand \left(7p^{2}\right)^{3}.

$$\frac{250047s^{9}a^{15}p^{12}}{7^{3}\left(p^{2}\right)^{3}\times \left(9s^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{250047s^{9}a^{15}p^{12}}{7^{3}p^{6}\times \left(9s^{2}\right)^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times \left(9s^{2}\right)^{3}}$$

Expand \left(9s^{2}\right)^{3}.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times 9^{3}\left(s^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times 9^{3}s^{6}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{250047s^{9}a^{15}p^{12}}{343p^{6}\times 729s^{6}}$$

Multiply 343 and 729 to get 250047.

$$\frac{250047s^{9}a^{15}p^{12}}{250047p^{6}s^{6}}$$

Cancel out 250047p^{6}s^{6} in both numerator and denominator.

$$s^{3}p^{6}a^{15}$$