Solve (3a^3)^3/(5a^6)^2

$$\frac { ( 3 a ^ { 3 } ) ^ { 3 } } { ( 5 a ^ { 6 } ) ^ { 2 } }$$

Evaluate

$$\frac{27}{25a^{3}}$$

Solution Steps

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

$$\frac{3^{3}\left(a^{3}\right)^{3}}{\left(5a^{6}\right)^{2}}$$

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

$$\frac{3^{3}a^{9}}{\left(5a^{6}\right)^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{9}}{\left(5a^{6}\right)^{2}}$$

Expand \left(5a^{6}\right)^{2}.

$$\frac{27a^{9}}{5^{2}\left(a^{6}\right)^{2}}$$

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

$$\frac{27a^{9}}{5^{2}a^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{27a^{9}}{25a^{12}}$$

Cancel out a^{9} in both numerator and denominator.

$$\frac{27}{25a^{3}}$$

Expand

$$\frac{27}{25a^{3}}$$

Solution Steps

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

$$\frac{3^{3}\left(a^{3}\right)^{3}}{\left(5a^{6}\right)^{2}}$$

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

$$\frac{3^{3}a^{9}}{\left(5a^{6}\right)^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{9}}{\left(5a^{6}\right)^{2}}$$

Expand \left(5a^{6}\right)^{2}.

$$\frac{27a^{9}}{5^{2}\left(a^{6}\right)^{2}}$$

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

$$\frac{27a^{9}}{5^{2}a^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{27a^{9}}{25a^{12}}$$

Cancel out a^{9} in both numerator and denominator.

$$\frac{27}{25a^{3}}$$