Solve (2a^3)^2(3a^3)^3

$$( 2 a ^ { 3 } ) ^ { 2 } ( 3 a ^ { 3 } ) ^ { 3 }$$

Evaluate

$$108a^{15}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply 3 times 2.

$$2^{2}\times 3^{3}a^{6}a^{3\times 3}$$

Multiply 3 times 3.

$$2^{2}\times 3^{3}a^{6}a^{9}$$

To multiply powers of the same base, add their exponents.

$$2^{2}\times 3^{3}a^{6+9}$$

Add the exponents 6 and 9.

$$2^{2}\times 3^{3}a^{15}$$

Raise 2 to the power 2.

$$4\times 3^{3}a^{15}$$

Raise 3 to the power 3.

$$4\times 27a^{15}$$

Multiply 4 times 27.

$$108a^{15}$$

Expand

$$108a^{15}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply 3 times 2.

$$2^{2}\times 3^{3}a^{6}a^{3\times 3}$$

Multiply 3 times 3.

$$2^{2}\times 3^{3}a^{6}a^{9}$$

To multiply powers of the same base, add their exponents.

$$2^{2}\times 3^{3}a^{6+9}$$

Add the exponents 6 and 9.

$$2^{2}\times 3^{3}a^{15}$$

Raise 2 to the power 2.

$$4\times 3^{3}a^{15}$$

Raise 3 to the power 3.

$$4\times 27a^{15}$$

Multiply 4 times 27.

$$108a^{15}$$