Solve (4a^3)^2a^5=

$$( 4 a ^ { 3 } ) ^ { 2 } a ^ { 5 } =$$

Evaluate

$$16a^{11}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4a^{3}\right)^{2}\left(a^{1}\right)^{5}$$

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

$$4^{2}\left(a^{3}\right)^{2}\times 1^{5}\left(a^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times 1^{5}\left(a^{3}\right)^{2}\left(a^{1}\right)^{5}$$

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

$$4^{2}\times 1^{5}a^{3\times 2}a^{5}$$

Multiply 3 times 2.

$$4^{2}\times 1^{5}a^{6}a^{5}$$

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

$$4^{2}\times 1^{5}a^{6+5}$$

Add the exponents 6 and 5.

$$4^{2}\times 1^{5}a^{11}$$

Raise 4 to the power 2.

$$16\times 1^{5}a^{11}$$

Expand

$$16a^{11}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4a^{3}\right)^{2}\left(a^{1}\right)^{5}$$

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

$$4^{2}\left(a^{3}\right)^{2}\times 1^{5}\left(a^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times 1^{5}\left(a^{3}\right)^{2}\left(a^{1}\right)^{5}$$

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

$$4^{2}\times 1^{5}a^{3\times 2}a^{5}$$

Multiply 3 times 2.

$$4^{2}\times 1^{5}a^{6}a^{5}$$

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

$$4^{2}\times 1^{5}a^{6+5}$$

Add the exponents 6 and 5.

$$4^{2}\times 1^{5}a^{11}$$

Raise 4 to the power 2.

$$16\times 1^{5}a^{11}$$