Solve (4v^5)^3/-2v^-2

$$\frac { ( 4 v ^ { 5 } ) ^ { 3 } } { - 2 v ^ { - 2 } }$$

Evaluate

$$-32v^{17}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4v^{5}\right)^{3}\times \frac{1}{-2v^{-2}}$$

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

$$4^{3}\left(v^{5}\right)^{3}\times \frac{1}{-2}\times \frac{1}{v^{-2}}$$

Use the Commutative Property of Multiplication.

$$4^{3}\times \frac{1}{-2}\left(v^{5}\right)^{3}\times \frac{1}{v^{-2}}$$

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

$$4^{3}\times \frac{1}{-2}v^{5\times 3}v^{-2\left(-1\right)}$$

Multiply 5 times 3.

$$4^{3}\times \frac{1}{-2}v^{15}v^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$4^{3}\times \frac{1}{-2}v^{15}v^{2}$$

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

$$4^{3}\times \frac{1}{-2}v^{15+2}$$

Add the exponents 15 and 2.

$$4^{3}\times \frac{1}{-2}v^{17}$$

Raise 4 to the power 3.

$$64\times \frac{1}{-2}v^{17}$$

Raise -2 to the power -1.

$$64\left(-\frac{1}{2}\right)v^{17}$$

Multiply 64 times -\frac{1}{2}.

$$-32v^{17}$$

Expand

$$-32v^{17}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4v^{5}\right)^{3}\times \frac{1}{-2v^{-2}}$$

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

$$4^{3}\left(v^{5}\right)^{3}\times \frac{1}{-2}\times \frac{1}{v^{-2}}$$

Use the Commutative Property of Multiplication.

$$4^{3}\times \frac{1}{-2}\left(v^{5}\right)^{3}\times \frac{1}{v^{-2}}$$

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

$$4^{3}\times \frac{1}{-2}v^{5\times 3}v^{-2\left(-1\right)}$$

Multiply 5 times 3.

$$4^{3}\times \frac{1}{-2}v^{15}v^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$4^{3}\times \frac{1}{-2}v^{15}v^{2}$$

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

$$4^{3}\times \frac{1}{-2}v^{15+2}$$

Add the exponents 15 and 2.

$$4^{3}\times \frac{1}{-2}v^{17}$$

Raise 4 to the power 3.

$$64\times \frac{1}{-2}v^{17}$$

Raise -2 to the power -1.

$$64\left(-\frac{1}{2}\right)v^{17}$$

Multiply 64 times -\frac{1}{2}.

$$-32v^{17}$$