Solve (w^3z)^2/z^2w^2=

$$\frac { ( w ^ { 3 } z ) ^ { 2 } } { z ^ { 2 } w ^ { 2 } } =$$

Evaluate

$$w^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(w^{3}z^{1}\right)^{2}\times \frac{1}{w^{2}z^{2}}$$

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

$$\left(w^{3}\right)^{2}\left(z^{1}\right)^{2}\times \frac{1}{w^{2}}\times \frac{1}{z^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(w^{3}\right)^{2}\times \frac{1}{w^{2}}\left(z^{1}\right)^{2}\times \frac{1}{z^{2}}$$

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

$$w^{3\times 2}w^{2\left(-1\right)}z^{2}z^{2\left(-1\right)}$$

Multiply 3 times 2.

$$w^{6}w^{2\left(-1\right)}z^{2}z^{2\left(-1\right)}$$

Multiply 2 times -1.

$$w^{6}w^{-2}z^{2}z^{2\left(-1\right)}$$

Multiply 2 times -1.

$$w^{6}w^{-2}z^{2}z^{-2}$$

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

$$w^{6-2}z^{2-2}$$

Add the exponents 6 and -2.

$$w^{4}z^{2-2}$$

Add the exponents 2 and -2.

$$w^{4}z^{0}$$

For any term t except 0, t^{0}=1.

$$w^{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$w^{4}$$

Expand

$$w^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(w^{3}z^{1}\right)^{2}\times \frac{1}{w^{2}z^{2}}$$

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

$$\left(w^{3}\right)^{2}\left(z^{1}\right)^{2}\times \frac{1}{w^{2}}\times \frac{1}{z^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(w^{3}\right)^{2}\times \frac{1}{w^{2}}\left(z^{1}\right)^{2}\times \frac{1}{z^{2}}$$

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

$$w^{3\times 2}w^{2\left(-1\right)}z^{2}z^{2\left(-1\right)}$$

Multiply 3 times 2.

$$w^{6}w^{2\left(-1\right)}z^{2}z^{2\left(-1\right)}$$

Multiply 2 times -1.

$$w^{6}w^{-2}z^{2}z^{2\left(-1\right)}$$

Multiply 2 times -1.

$$w^{6}w^{-2}z^{2}z^{-2}$$

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

$$w^{6-2}z^{2-2}$$

Add the exponents 6 and -2.

$$w^{4}z^{2-2}$$

Add the exponents 2 and -2.

$$w^{4}z^{0}$$

For any term t except 0, t^{0}=1.

$$w^{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$w^{4}$$