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

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

Evaluate

$$4a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2a^{1}\right)^{2}\left(a^{2}\right)^{3}$$

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

$$2^{2}\left(a^{1}\right)^{2}\times 1^{3}\left(a^{2}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$2^{2}\times 1^{3}\left(a^{1}\right)^{2}\left(a^{2}\right)^{3}$$

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

$$2^{2}\times 1^{3}a^{2}a^{2\times 3}$$

Multiply 2 times 3.

$$2^{2}\times 1^{3}a^{2}a^{6}$$

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

$$2^{2}\times 1^{3}a^{2+6}$$

Add the exponents 2 and 6.

$$2^{2}\times 1^{3}a^{8}$$

Raise 2 to the power 2.

$$4\times 1^{3}a^{8}$$

Expand

$$4a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2a^{1}\right)^{2}\left(a^{2}\right)^{3}$$

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

$$2^{2}\left(a^{1}\right)^{2}\times 1^{3}\left(a^{2}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$2^{2}\times 1^{3}\left(a^{1}\right)^{2}\left(a^{2}\right)^{3}$$

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

$$2^{2}\times 1^{3}a^{2}a^{2\times 3}$$

Multiply 2 times 3.

$$2^{2}\times 1^{3}a^{2}a^{6}$$

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

$$2^{2}\times 1^{3}a^{2+6}$$

Add the exponents 2 and 6.

$$2^{2}\times 1^{3}a^{8}$$

Raise 2 to the power 2.

$$4\times 1^{3}a^{8}$$