Simplify (39x^5z^4)^0*18x^2y

${(39 x^{5} z^{4})}^{0} \cdot 18 x^{2} y$

Step 1

Rewrite using the commutative property of multiplication.

$18 {(39 x^{5} z^{4})}^{0} x^{2} y$

Step 2

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

Apply the product rule to $39 x^{5} z^{4}$ .

$18 ({(39 x^{5})}^{0} {(z^{4})}^{0}) x^{2} y$

Apply the product rule to $39 x^{5}$ .

$18 (39^{0} {(x^{5})}^{0} {(z^{4})}^{0}) x^{2} y$

Step 3

Anything raised to $0$ is $1$ .

$18 (1 {(x^{5})}^{0} {(z^{4})}^{0}) x^{2} y$

Step 4

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

$18 ({(x^{5})}^{0} {(z^{4})}^{0}) x^{2} y$

Step 5

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

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

$18 (x^{5 \cdot 0} {(z^{4})}^{0}) x^{2} y$

Multiply $5$ by $0$ .

$18 (x^{0} {(z^{4})}^{0}) x^{2} y$

Step 6

Multiply $x^{0}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$18 (x^{2} x^{0} {(z^{4})}^{0}) y$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$18 (x^{2 + 0} {(z^{4})}^{0}) y$

Add $2$ and $0$ .

$18 (x^{2} {(z^{4})}^{0}) y$

Step 7

Simplify $18 (x^{2} {(z^{4})}^{0}) y$ .

$18 x^{2} y$