Simplify (yx^2)^4*(x^3y^4)^0

${(y x^{2})}^{4} \cdot {(x^{3} y^{4})}^{0}$

Step 1

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

$y^{4} {(x^{2})}^{4} \cdot {(x^{3} y^{4})}^{0}$

Step 2

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$y^{4} x^{2 \cdot 4} \cdot {(x^{3} y^{4})}^{0}$

Multiply $2$ by $4$ .

$y^{4} x^{8} \cdot {(x^{3} y^{4})}^{0}$

Step 3

Apply the product rule to $x^{3} y^{4}$ .

$y^{4} x^{8} \cdot ({(x^{3})}^{0} {(y^{4})}^{0})$

Step 4

Multiply the exponents in ${(x^{3})}^{0}$ .

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

$y^{4} x^{8} \cdot (x^{3 \cdot 0} {(y^{4})}^{0})$

Multiply $3$ by $0$ .

$y^{4} x^{8} \cdot (x^{0} {(y^{4})}^{0})$

Step 5

Multiply $x^{8}$ by $x^{0}$ by adding the exponents.

Move $x^{0}$ .

$y^{4} (x^{0} x^{8}) \cdot {(y^{4})}^{0}$

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

$y^{4} x^{0 + 8} \cdot {(y^{4})}^{0}$

Add $0$ and $8$ .

$y^{4} x^{8} \cdot {(y^{4})}^{0}$

Step 6

Simplify $y^{4} x^{8} \cdot {(y^{4})}^{0}$ .

$y^{4} x^{8}$