Evaluate (5x^2y^5z^7)^0

${(5 x^{2} y^{5} z^{7})}^{0}$

Step 1

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

Apply the product rule to $5 x^{2} y^{5} z^{7}$ .

${(5 x^{2} y^{5})}^{0} {(z^{7})}^{0}$

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

${(5 x^{2})}^{0} {(y^{5})}^{0} {(z^{7})}^{0}$

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

$5^{0} {(x^{2})}^{0} {(y^{5})}^{0} {(z^{7})}^{0}$

Step 2

Anything raised to $0$ is $1$ .

$1 {(x^{2})}^{0} {(y^{5})}^{0} {(z^{7})}^{0}$

Step 3

Multiply ${(x^{2})}^{0}$ by $1$ .

${(x^{2})}^{0} {(y^{5})}^{0} {(z^{7})}^{0}$

Step 4

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

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

$x^{2 \cdot 0} {(y^{5})}^{0} {(z^{7})}^{0}$

Multiply $2$ by $0$ .

$x^{0} {(y^{5})}^{0} {(z^{7})}^{0}$

Step 5

Anything raised to $0$ is $1$ .

$1 {(y^{5})}^{0} {(z^{7})}^{0}$

Step 6

Multiply ${(y^{5})}^{0}$ by $1$ .

${(y^{5})}^{0} {(z^{7})}^{0}$

Step 7

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

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

$y^{5 \cdot 0} {(z^{7})}^{0}$

Multiply $5$ by $0$ .

$y^{0} {(z^{7})}^{0}$

Step 8

Anything raised to $0$ is $1$ .

$1 {(z^{7})}^{0}$

Step 9

Multiply ${(z^{7})}^{0}$ by $1$ .

${(z^{7})}^{0}$

Step 10

Multiply the exponents in ${(z^{7})}^{0}$ .

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

$z^{7 \cdot 0}$

Multiply $7$ by $0$ .

$z^{0}$

Step 11

Anything raised to $0$ is $1$ .

$1$

Evaluate (5x^2y^5z^7)^0

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