Solve (3x)^2(4x^7)^2

$$( 3 x ) ^ { 2 } ( 4 x ^ { 7 } ) ^ { 2 }$$

Evaluate

$$144x^{16}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3x^{1}\right)^{2}\times \left(4x^{7}\right)^{2}$$

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

$$3^{2}\left(x^{1}\right)^{2}\times 4^{2}\left(x^{7}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$3^{2}\times 4^{2}\left(x^{1}\right)^{2}\left(x^{7}\right)^{2}$$

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

$$3^{2}\times 4^{2}x^{2}x^{7\times 2}$$

Multiply 7 times 2.

$$3^{2}\times 4^{2}x^{2}x^{14}$$

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

$$3^{2}\times 4^{2}x^{2+14}$$

Add the exponents 2 and 14.

$$3^{2}\times 4^{2}x^{16}$$

Raise 3 to the power 2.

$$9\times 4^{2}x^{16}$$

Raise 4 to the power 2.

$$9\times 16x^{16}$$

Multiply 9 times 16.

$$144x^{16}$$

Expand

$$144x^{16}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3x^{1}\right)^{2}\times \left(4x^{7}\right)^{2}$$

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

$$3^{2}\left(x^{1}\right)^{2}\times 4^{2}\left(x^{7}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$3^{2}\times 4^{2}\left(x^{1}\right)^{2}\left(x^{7}\right)^{2}$$

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

$$3^{2}\times 4^{2}x^{2}x^{7\times 2}$$

Multiply 7 times 2.

$$3^{2}\times 4^{2}x^{2}x^{14}$$

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

$$3^{2}\times 4^{2}x^{2+14}$$

Add the exponents 2 and 14.

$$3^{2}\times 4^{2}x^{16}$$

Raise 3 to the power 2.

$$9\times 4^{2}x^{16}$$

Raise 4 to the power 2.

$$9\times 16x^{16}$$

Multiply 9 times 16.

$$144x^{16}$$