Solve frac{(3a^{3})^{2}+2a^4*3a^2}{(2a^2)^2}

$$\frac { ( 3 a ^ { 3 } ) ^ { 2 } + 2 a ^ { 4 } \times 3 a ^ { 2 } } { ( 2 a ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{15a^{2}}{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 2 and 3 to get 6.

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

Combine 9a^{6} and 6a^{6} to get 15a^{6}.

$$\frac{15a^{6}}{\left(2a^{2}\right)^{2}}$$

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

$$\frac{15a^{6}}{2^{2}\left(a^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{15a^{6}}{2^{2}a^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{15a^{6}}{4a^{4}}$$

Cancel out a^{4} in both numerator and denominator.

$$\frac{15a^{2}}{4}$$

Expand

$$\frac{15a^{2}}{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 2 and 3 to get 6.

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

Combine 9a^{6} and 6a^{6} to get 15a^{6}.

$$\frac{15a^{6}}{\left(2a^{2}\right)^{2}}$$

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

$$\frac{15a^{6}}{2^{2}\left(a^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{15a^{6}}{2^{2}a^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{15a^{6}}{4a^{4}}$$

Cancel out a^{4} in both numerator and denominator.

$$\frac{15a^{2}}{4}$$