Solve (4x)^2/x^-5

$$\frac { ( 4 x ) ^ { 2 } } { x ^ { - 5 } }$$

Evaluate

$$16x^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4x^{1}\right)^{2}\times \frac{1}{x^{-5}}$$

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

$$4^{2}\left(x^{1}\right)^{2}\times \frac{1}{1}\times \frac{1}{x^{-5}}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times \frac{1}{1}\left(x^{1}\right)^{2}\times \frac{1}{x^{-5}}$$

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

$$4^{2}\times \frac{1}{1}x^{2}x^{-5\left(-1\right)}$$

Multiply -5 times -1.

$$4^{2}\times \frac{1}{1}x^{2}x^{5}$$

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

$$4^{2}\times \frac{1}{1}x^{2+5}$$

Add the exponents 2 and 5.

$$4^{2}\times \frac{1}{1}x^{7}$$

Raise 4 to the power 2.

$$16\times \frac{1}{1}x^{7}$$

Expand

$$16x^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4x^{1}\right)^{2}\times \frac{1}{x^{-5}}$$

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

$$4^{2}\left(x^{1}\right)^{2}\times \frac{1}{1}\times \frac{1}{x^{-5}}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times \frac{1}{1}\left(x^{1}\right)^{2}\times \frac{1}{x^{-5}}$$

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

$$4^{2}\times \frac{1}{1}x^{2}x^{-5\left(-1\right)}$$

Multiply -5 times -1.

$$4^{2}\times \frac{1}{1}x^{2}x^{5}$$

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

$$4^{2}\times \frac{1}{1}x^{2+5}$$

Add the exponents 2 and 5.

$$4^{2}\times \frac{1}{1}x^{7}$$

Raise 4 to the power 2.

$$16\times \frac{1}{1}x^{7}$$