Solve frac{(w^{-4}z^-2)^2}{w^-3z^5}

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

Evaluate

$$\frac{1}{w^{5}z^{9}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -4 times 2.

$$w^{-8}w^{-3\left(-1\right)}z^{-2\times 2}z^{5\left(-1\right)}$$

Multiply -3 times -1.

$$w^{-8}w^{3}z^{-2\times 2}z^{5\left(-1\right)}$$

Multiply -2 times 2.

$$w^{-8}w^{3}z^{-4}z^{5\left(-1\right)}$$

Multiply 5 times -1.

$$w^{-8}w^{3}z^{-4}z^{-5}$$

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

$$w^{-8+3}z^{-4-5}$$

Add the exponents -8 and 3.

$$w^{-5}z^{-4-5}$$

Add the exponents -4 and -5.

$$w^{-5}z^{-9}$$

Expand

$$\frac{1}{w^{5}z^{9}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -4 times 2.

$$w^{-8}w^{-3\left(-1\right)}z^{-2\times 2}z^{5\left(-1\right)}$$

Multiply -3 times -1.

$$w^{-8}w^{3}z^{-2\times 2}z^{5\left(-1\right)}$$

Multiply -2 times 2.

$$w^{-8}w^{3}z^{-4}z^{5\left(-1\right)}$$

Multiply 5 times -1.

$$w^{-8}w^{3}z^{-4}z^{-5}$$

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

$$w^{-8+3}z^{-4-5}$$

Add the exponents -8 and 3.

$$w^{-5}z^{-4-5}$$

Add the exponents -4 and -5.

$$w^{-5}z^{-9}$$