Solve (+3a^{4})(+3a^{4})^{2}(+3a^4)^3:(+3a^4)^3

$$( + 3 a ^ { 4 } ) ( + 3 a ^ { 4 } ) ^ { 2 } ( + 3 a ^ { 4 } ) ^ { 3 } : ( + 3 a ^ { 4 } ) ^ { 3 }$$

Evaluate

$$27a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

Cancel out \left(3a^{4}\right)^{3} in both numerator and denominator.

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

Expand \left(3a^{4}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$3a^{4}\times 3^{2}a^{8}$$

Calculate 3 to the power of 2 and get 9.

$$3a^{4}\times 9a^{8}$$

Multiply 3 and 9 to get 27.

$$27a^{4}a^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$27a^{12}$$

Expand

$$27a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

Cancel out \left(3a^{4}\right)^{3} in both numerator and denominator.

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

Expand \left(3a^{4}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$3a^{4}\times 3^{2}a^{8}$$

Calculate 3 to the power of 2 and get 9.

$$3a^{4}\times 9a^{8}$$

Multiply 3 and 9 to get 27.

$$27a^{4}a^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$27a^{12}$$