Solve (2x^2)^3(4x)^2

$$( 2 x ^ { 2 } ) ^ { 3 } ( 4 x ) ^ { 2 }$$

Evaluate

$$128x^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$2^{3}\times 4^{2}x^{2\times 3}x^{2}$$

Multiply 2 times 3.

$$2^{3}\times 4^{2}x^{6}x^{2}$$

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

$$2^{3}\times 4^{2}x^{6+2}$$

Add the exponents 6 and 2.

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

Raise 2 to the power 3.

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

Raise 4 to the power 2.

$$8\times 16x^{8}$$

Multiply 8 times 16.

$$128x^{8}$$

Expand

$$128x^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$2^{3}\times 4^{2}x^{2\times 3}x^{2}$$

Multiply 2 times 3.

$$2^{3}\times 4^{2}x^{6}x^{2}$$

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

$$2^{3}\times 4^{2}x^{6+2}$$

Add the exponents 6 and 2.

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

Raise 2 to the power 3.

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

Raise 4 to the power 2.

$$8\times 16x^{8}$$

Multiply 8 times 16.

$$128x^{8}$$