Solve (3y^3)^2/6y^7

$$\frac { ( 3 y ^ { 3 } ) ^ { 2 } } { 6 y ^ { 7 } }$$

Evaluate

$$\frac{3}{2y}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3y^{3}\right)^{2}\times \frac{1}{6y^{7}}$$

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

$$3^{2}\left(y^{3}\right)^{2}\times \frac{1}{6}\times \frac{1}{y^{7}}$$

Use the Commutative Property of Multiplication.

$$3^{2}\times \frac{1}{6}\left(y^{3}\right)^{2}\times \frac{1}{y^{7}}$$

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

$$3^{2}\times \frac{1}{6}y^{3\times 2}y^{7\left(-1\right)}$$

Multiply 3 times 2.

$$3^{2}\times \frac{1}{6}y^{6}y^{7\left(-1\right)}$$

Multiply 7 times -1.

$$3^{2}\times \frac{1}{6}y^{6}y^{-7}$$

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

$$3^{2}\times \frac{1}{6}y^{6-7}$$

Add the exponents 6 and -7.

$$3^{2}\times \frac{1}{6}\times \frac{1}{y}$$

Raise 3 to the power 2.

$$9\times \frac{1}{6}\times \frac{1}{y}$$

Multiply 9 times \frac{1}{6}.

$$\frac{3}{2}\times \frac{1}{y}$$

Expand

$$\frac{3}{2y}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3y^{3}\right)^{2}\times \frac{1}{6y^{7}}$$

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

$$3^{2}\left(y^{3}\right)^{2}\times \frac{1}{6}\times \frac{1}{y^{7}}$$

Use the Commutative Property of Multiplication.

$$3^{2}\times \frac{1}{6}\left(y^{3}\right)^{2}\times \frac{1}{y^{7}}$$

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

$$3^{2}\times \frac{1}{6}y^{3\times 2}y^{7\left(-1\right)}$$

Multiply 3 times 2.

$$3^{2}\times \frac{1}{6}y^{6}y^{7\left(-1\right)}$$

Multiply 7 times -1.

$$3^{2}\times \frac{1}{6}y^{6}y^{-7}$$

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

$$3^{2}\times \frac{1}{6}y^{6-7}$$

Add the exponents 6 and -7.

$$3^{2}\times \frac{1}{6}\times \frac{1}{y}$$

Raise 3 to the power 2.

$$9\times \frac{1}{6}\times \frac{1}{y}$$

Multiply 9 times \frac{1}{6}.

$$\frac{3}{2}\times \frac{1}{y}$$