Solve (2x^8)^2/x^-4=

$$\frac { ( 2 x ^ { 8 } ) ^ { 2 } } { x ^ { - 4 } } =$$

Evaluate

$$4x^{20}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2x^{8}\right)^{2}\times \frac{1}{x^{-4}}$$

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

$$2^{2}\left(x^{8}\right)^{2}\times \frac{1}{1}\times \frac{1}{x^{-4}}$$

Use the Commutative Property of Multiplication.

$$2^{2}\times \frac{1}{1}\left(x^{8}\right)^{2}\times \frac{1}{x^{-4}}$$

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

$$2^{2}\times \frac{1}{1}x^{8\times 2}x^{-4\left(-1\right)}$$

Multiply 8 times 2.

$$2^{2}\times \frac{1}{1}x^{16}x^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$2^{2}\times \frac{1}{1}x^{16}x^{4}$$

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

$$2^{2}\times \frac{1}{1}x^{16+4}$$

Add the exponents 16 and 4.

$$2^{2}\times \frac{1}{1}x^{20}$$

Raise 2 to the power 2.

$$4\times \frac{1}{1}x^{20}$$

Expand

$$4x^{20}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2x^{8}\right)^{2}\times \frac{1}{x^{-4}}$$

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

$$2^{2}\left(x^{8}\right)^{2}\times \frac{1}{1}\times \frac{1}{x^{-4}}$$

Use the Commutative Property of Multiplication.

$$2^{2}\times \frac{1}{1}\left(x^{8}\right)^{2}\times \frac{1}{x^{-4}}$$

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

$$2^{2}\times \frac{1}{1}x^{8\times 2}x^{-4\left(-1\right)}$$

Multiply 8 times 2.

$$2^{2}\times \frac{1}{1}x^{16}x^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$2^{2}\times \frac{1}{1}x^{16}x^{4}$$

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

$$2^{2}\times \frac{1}{1}x^{16+4}$$

Add the exponents 16 and 4.

$$2^{2}\times \frac{1}{1}x^{20}$$

Raise 2 to the power 2.

$$4\times \frac{1}{1}x^{20}$$