Simplify (s^4t)^2(st)

${(s^{4} t)}^{2} (s t)$

Step 1

Apply the product rule to $s^{4} t$ .

${(s^{4})}^{2} t^{2} (s t)$

Step 2

Multiply $t^{2}$ by $t$ by adding the exponents.

Move $t$ .

${(s^{4})}^{2} (t \cdot t^{2}) s$

Multiply $t$ by $t^{2}$ .

Raise $t$ to the power of $1$ .

${(s^{4})}^{2} (t^{1} t^{2}) s$

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

${(s^{4})}^{2} t^{1 + 2} s$

Add $1$ and $2$ .

${(s^{4})}^{2} t^{3} s$

Step 3

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

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

$s^{4 \cdot 2} t^{3} s$

Multiply $4$ by $2$ .

$s^{8} t^{3} s$

Step 4

Multiply $s^{8}$ by $s$ by adding the exponents.

Move $s$ .

$s \cdot s^{8} t^{3}$

Multiply $s$ by $s^{8}$ .

Raise $s$ to the power of $1$ .

$s^{1} s^{8} t^{3}$

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

$s^{1 + 8} t^{3}$

Add $1$ and $8$ .

$s^{9} t^{3}$