Simplify ((5x^13y^5z^2)/(3*5^2))^0

${(\frac{5 x^{13} y^{5} z^{2}}{3 \cdot 5^{2}})}^{0}$

Step 1

Cancel the common factor of $5$ and $5^{2}$ .

Factor $5$ out of $5 x^{13} y^{5} z^{2}$ .

${(\frac{5 (x^{13} y^{5} z^{2})}{3 \cdot 5^{2}})}^{0}$

Cancel the common factors.

Factor $5$ out of $3 \cdot 5^{2}$ .

${(\frac{5 (x^{13} y^{5} z^{2})}{5 (3 \cdot 5)})}^{0}$

Cancel the common factor.

${(\frac{5 (x^{13} y^{5} z^{2})}{5 (3 \cdot 5)})}^{0}$

Rewrite the expression.

${(\frac{x^{13} y^{5} z^{2}}{3 \cdot 5})}^{0}$

Step 2

Multiply $3$ by $5$ .

${(\frac{x^{13} y^{5} z^{2}}{15})}^{0}$

Step 3

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

Apply the product rule to $\frac{x^{13} y^{5} z^{2}}{15}$ .

$\frac{{(x^{13} y^{5} z^{2})}^{0}}{15^{0}}$

Apply the product rule to $x^{13} y^{5} z^{2}$ .

$\frac{{(x^{13} y^{5})}^{0} {(z^{2})}^{0}}{15^{0}}$

Apply the product rule to $x^{13} y^{5}$ .

$\frac{{(x^{13})}^{0} {(y^{5})}^{0} {(z^{2})}^{0}}{15^{0}}$

Step 4

Simplify the numerator.

Multiply the exponents in ${(x^{13})}^{0}$ .

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

$\frac{x^{13 \cdot 0} {(y^{5})}^{0} {(z^{2})}^{0}}{15^{0}}$

Multiply $13$ by $0$ .

$\frac{x^{0} {(y^{5})}^{0} {(z^{2})}^{0}}{15^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 {(y^{5})}^{0} {(z^{2})}^{0}}{15^{0}}$

Multiply the exponents in ${(y^{5})}^{0}$ .

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

$\frac{1 y^{5 \cdot 0} {(z^{2})}^{0}}{15^{0}}$

Multiply $5$ by $0$ .

$\frac{1 y^{0} {(z^{2})}^{0}}{15^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 {(z^{2})}^{0}}{15^{0}}$

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

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

$\frac{1 \cdot 1 z^{2 \cdot 0}}{15^{0}}$

Multiply $2$ by $0$ .

$\frac{1 \cdot 1 z^{0}}{15^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 \cdot 1}{15^{0}}$

Combine exponents.

Multiply $1$ by $1$ .

$\frac{1 \cdot 1}{15^{0}}$

Multiply $1$ by $1$ .

$\frac{1}{15^{0}}$

Step 5

Simplify the expression.

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$

Simplify ((5x^13y^5z^2)/(3*5^2))^0

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