Solve frac{(6a^{4})^5}{(2a^2)^2(3a^3)}

$$\frac { ( 6 a ^ { 4 } ) ^ { 5 } } { ( 2 a ^ { 2 } ) ^ { 2 } ( 3 a ^ { 3 } ) }$$

Evaluate

$$648a^{13}$$

Solution Steps

Expand \left(6a^{4}\right)^{5}.

$$\frac{6^{5}\left(a^{4}\right)^{5}}{\left(2a^{2}\right)^{2}\times 3a^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{6^{5}a^{20}}{\left(2a^{2}\right)^{2}\times 3a^{3}}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{7776a^{20}}{\left(2a^{2}\right)^{2}\times 3a^{3}}$$

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

$$\frac{7776a^{20}}{2^{2}\left(a^{2}\right)^{2}\times 3a^{3}}$$

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

$$\frac{7776a^{20}}{2^{2}a^{4}\times 3a^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{7776a^{20}}{4a^{4}\times 3a^{3}}$$

Multiply 4 and 3 to get 12.

$$\frac{7776a^{20}}{12a^{4}a^{3}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{7776a^{20}}{12a^{7}}$$

Cancel out 12a^{7} in both numerator and denominator.

$$648a^{13}$$

Expand

$$648a^{13}$$

Solution Steps

Expand \left(6a^{4}\right)^{5}.

$$\frac{6^{5}\left(a^{4}\right)^{5}}{\left(2a^{2}\right)^{2}\times 3a^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{6^{5}a^{20}}{\left(2a^{2}\right)^{2}\times 3a^{3}}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{7776a^{20}}{\left(2a^{2}\right)^{2}\times 3a^{3}}$$

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

$$\frac{7776a^{20}}{2^{2}\left(a^{2}\right)^{2}\times 3a^{3}}$$

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

$$\frac{7776a^{20}}{2^{2}a^{4}\times 3a^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{7776a^{20}}{4a^{4}\times 3a^{3}}$$

Multiply 4 and 3 to get 12.

$$\frac{7776a^{20}}{12a^{4}a^{3}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{7776a^{20}}{12a^{7}}$$

Cancel out 12a^{7} in both numerator and denominator.

$$648a^{13}$$