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

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

Evaluate

$$27y^{14}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 4 times 3.

$$3^{3}\times \frac{1}{1}y^{12}y^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$3^{3}\times \frac{1}{1}y^{12}y^{2}$$

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

$$3^{3}\times \frac{1}{1}y^{12+2}$$

Add the exponents 12 and 2.

$$3^{3}\times \frac{1}{1}y^{14}$$

Raise 3 to the power 3.

$$27\times \frac{1}{1}y^{14}$$

Expand

$$27y^{14}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 4 times 3.

$$3^{3}\times \frac{1}{1}y^{12}y^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$3^{3}\times \frac{1}{1}y^{12}y^{2}$$

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

$$3^{3}\times \frac{1}{1}y^{12+2}$$

Add the exponents 12 and 2.

$$3^{3}\times \frac{1}{1}y^{14}$$

Raise 3 to the power 3.

$$27\times \frac{1}{1}y^{14}$$