Simplify (s^4tu^2)(s^7t^-1)

$(s^{4} t u^{2}) (s^{7} t^{- 1})$

Step 1

Multiply $s^{4}$ by $s^{7}$ by adding the exponents.

Move $s^{7}$ .

$s^{7} s^{4} t u^{2} t^{- 1}$

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

$s^{7 + 4} t u^{2} t^{- 1}$

Add $7$ and $4$ .

$s^{11} t u^{2} t^{- 1}$

Step 2

Multiply $t$ by $t^{- 1}$ by adding the exponents.

Move $t^{- 1}$ .

$s^{11} (t^{- 1} t) u^{2}$

Multiply $t^{- 1}$ by $t$ .

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

$s^{11} (t^{- 1} t^{1}) u^{2}$

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

$s^{11} t^{- 1 + 1} u^{2}$

Add $- 1$ and $1$ .

$s^{11} t^{0} u^{2}$

Step 3

Simplify $s^{11} t^{0} u^{2}$ .

$s^{11} u^{2}$