Solve (4y^5)^3/2y^5

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

Evaluate

$$32y^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 5 times 3.

$$4^{3}\times \frac{1}{2}y^{15}y^{5\left(-1\right)}$$

Multiply 5 times -1.

$$4^{3}\times \frac{1}{2}y^{15}y^{-5}$$

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

$$4^{3}\times \frac{1}{2}y^{15-5}$$

Add the exponents 15 and -5.

$$4^{3}\times \frac{1}{2}y^{10}$$

Raise 4 to the power 3.

$$64\times \frac{1}{2}y^{10}$$

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

$$32y^{10}$$

Expand

$$32y^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 5 times 3.

$$4^{3}\times \frac{1}{2}y^{15}y^{5\left(-1\right)}$$

Multiply 5 times -1.

$$4^{3}\times \frac{1}{2}y^{15}y^{-5}$$

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

$$4^{3}\times \frac{1}{2}y^{15-5}$$

Add the exponents 15 and -5.

$$4^{3}\times \frac{1}{2}y^{10}$$

Raise 4 to the power 3.

$$64\times \frac{1}{2}y^{10}$$

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

$$32y^{10}$$