Simplify ((16p^5w^2)/(2p^3w^3))^0

${(\frac{16 p^{5} w^{2}}{2 p^{3} w^{3}})}^{0}$

Step 1

Cancel the common factor of $16$ and $2$ .

Factor $2$ out of $16 p^{5} w^{2}$ .

${(\frac{2 (8 p^{5} w^{2})}{2 p^{3} w^{3}})}^{0}$

Cancel the common factors.

Factor $2$ out of $2 p^{3} w^{3}$ .

${(\frac{2 (8 p^{5} w^{2})}{2 (p^{3} w^{3})})}^{0}$

Cancel the common factor.

${(\frac{2 (8 p^{5} w^{2})}{2 (p^{3} w^{3})})}^{0}$

Rewrite the expression.

${(\frac{8 p^{5} w^{2}}{p^{3} w^{3}})}^{0}$

Step 2

Cancel the common factor of $p^{5}$ and $p^{3}$ .

Factor $p^{3}$ out of $8 p^{5} w^{2}$ .

${(\frac{p^{3} (8 p^{2} w^{2})}{p^{3} w^{3}})}^{0}$

Cancel the common factors.

Factor $p^{3}$ out of $p^{3} w^{3}$ .

${(\frac{p^{3} (8 p^{2} w^{2})}{p^{3} (w^{3})})}^{0}$

Cancel the common factor.

${(\frac{p^{3} (8 p^{2} w^{2})}{p^{3} w^{3}})}^{0}$

Rewrite the expression.

${(\frac{8 p^{2} w^{2}}{w^{3}})}^{0}$

Step 3

Cancel the common factor of $w^{2}$ and $w^{3}$ .

Factor $w^{2}$ out of $8 p^{2} w^{2}$ .

${(\frac{w^{2} (8 p^{2})}{w^{3}})}^{0}$

Cancel the common factors.

Factor $w^{2}$ out of $w^{3}$ .

${(\frac{w^{2} (8 p^{2})}{w^{2} w})}^{0}$

Cancel the common factor.

${(\frac{w^{2} (8 p^{2})}{w^{2} w})}^{0}$

Rewrite the expression.

${(\frac{8 p^{2}}{w})}^{0}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{8 p^{2}}{w}$ .

$\frac{{(8 p^{2})}^{0}}{w^{0}}$

Apply the product rule to $8 p^{2}$ .

$\frac{8^{0} {(p^{2})}^{0}}{w^{0}}$

Step 5

Simplify the numerator.

Anything raised to $0$ is $1$ .

$\frac{1 {(p^{2})}^{0}}{w^{0}}$

Multiply the exponents in ${(p^{2})}^{0}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1 p^{2 \cdot 0}}{w^{0}}$

Multiply $2$ by $0$ .

$\frac{1 p^{0}}{w^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{w^{0}}$

Multiply $1$ by $1$ .

$\frac{1}{w^{0}}$

Step 6

Simplify the expression.

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$

Simplify ((16p^5w^2)/(2p^3w^3))^0

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