Solve (8a^4)^2(2a)^4

$$( 8 a ^ { 4 } ) ^ { 2 } ( 2 a ) ^ { 4 }$$

Evaluate

$$1024a^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8a^{4}\right)^{2}\times \left(2a^{1}\right)^{4}$$

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

$$8^{2}\left(a^{4}\right)^{2}\times 2^{4}\left(a^{1}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$8^{2}\times 2^{4}\left(a^{4}\right)^{2}\left(a^{1}\right)^{4}$$

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

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

Multiply 4 times 2.

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

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

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

Add the exponents 8 and 4.

$$8^{2}\times 2^{4}a^{12}$$

Raise 8 to the power 2.

$$64\times 2^{4}a^{12}$$

Raise 2 to the power 4.

$$64\times 16a^{12}$$

Multiply 64 times 16.

$$1024a^{12}$$

Expand

$$1024a^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8a^{4}\right)^{2}\times \left(2a^{1}\right)^{4}$$

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

$$8^{2}\left(a^{4}\right)^{2}\times 2^{4}\left(a^{1}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$8^{2}\times 2^{4}\left(a^{4}\right)^{2}\left(a^{1}\right)^{4}$$

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

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

Multiply 4 times 2.

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

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

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

Add the exponents 8 and 4.

$$8^{2}\times 2^{4}a^{12}$$

Raise 8 to the power 2.

$$64\times 2^{4}a^{12}$$

Raise 2 to the power 4.

$$64\times 16a^{12}$$

Multiply 64 times 16.

$$1024a^{12}$$