Solve (2x_0^2)^4x_{0}

$$( 2 x _ { 0 } ^ { 2 } ) ^ { 4 } x _ { 0 }$$

Evaluate

$$16x_{0}^{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2x_{0}^{2}\right)^{4}\left(x_{0}^{1}\right)^{1}$$

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

$$2^{4}\left(x_{0}^{2}\right)^{4}\times 1^{1}\left(x_{0}^{1}\right)^{1}$$

Use the Commutative Property of Multiplication.

$$2^{4}\times 1^{1}\left(x_{0}^{2}\right)^{4}\left(x_{0}^{1}\right)^{1}$$

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

$$2^{4}\times 1^{1}x_{0}^{2\times 4}x_{0}^{1}$$

Multiply 2 times 4.

$$2^{4}\times 1^{1}x_{0}^{8}x_{0}^{1}$$

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

$$2^{4}\times 1^{1}x_{0}^{8+1}$$

Add the exponents 8 and 1.

$$2^{4}\times 1^{1}x_{0}^{9}$$

Raise 2 to the power 4.

$$16\times 1^{1}x_{0}^{9}$$

For any term t, t^{1}=t.

$$16\times 1x_{0}^{9}$$

For any term t, t\times 1=t and 1t=t.

$$16x_{0}^{9}$$

Expand

$$16x_{0}^{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2x_{0}^{2}\right)^{4}\left(x_{0}^{1}\right)^{1}$$

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

$$2^{4}\left(x_{0}^{2}\right)^{4}\times 1^{1}\left(x_{0}^{1}\right)^{1}$$

Use the Commutative Property of Multiplication.

$$2^{4}\times 1^{1}\left(x_{0}^{2}\right)^{4}\left(x_{0}^{1}\right)^{1}$$

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

$$2^{4}\times 1^{1}x_{0}^{2\times 4}x_{0}^{1}$$

Multiply 2 times 4.

$$2^{4}\times 1^{1}x_{0}^{8}x_{0}^{1}$$

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

$$2^{4}\times 1^{1}x_{0}^{8+1}$$

Add the exponents 8 and 1.

$$2^{4}\times 1^{1}x_{0}^{9}$$

Raise 2 to the power 4.

$$16\times 1^{1}x_{0}^{9}$$

For any term t, t^{1}=t.

$$16\times 1x_{0}^{9}$$

For any term t, t\times 1=t and 1t=t.

$$16x_{0}^{9}$$