Precalculus Examples

$(2 s^{3} t^{- 1}) (\frac{1}{4} s^{6}) (16 t^{4})$

Step 1

Multiply $s^{3}$ by $s^{6}$ by adding the exponents.

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Step 1.1

Move $s^{6}$ .

$2 (s^{6} s^{3}) t^{- 1} \frac{1}{4} (16 t^{4})$

Step 1.2

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

$2 s^{6 + 3} t^{- 1} \frac{1}{4} (16 t^{4})$

Step 1.3

Add $6$ and $3$ .

$2 s^{9} t^{- 1} \frac{1}{4} (16 t^{4})$

Step 2

Multiply $t^{- 1}$ by $t^{4}$ by adding the exponents.

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Step 2.1

Move $t^{4}$ .

$2 s^{9} (t^{4} t^{- 1}) \frac{1}{4} \cdot 16$

Step 2.2

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

$2 s^{9} t^{4 - 1} \frac{1}{4} \cdot 16$

Step 2.3

Subtract $1$ from $4$ .

$2 s^{9} t^{3} \frac{1}{4} \cdot 16$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $2 s^{9} t^{3}$ .

$2 (s^{9} t^{3}) \frac{1}{4} \cdot 16$

Step 3.2

Factor $2$ out of $4$ .

$2 (s^{9} t^{3}) \frac{1}{2 (2)} \cdot 16$

Step 3.3

Cancel the common factor.

$2 (s^{9} t^{3}) \frac{1}{2 \cdot 2} \cdot 16$

Step 3.4

Rewrite the expression.

$s^{9} t^{3} \frac{1}{2} \cdot 16$

Step 4

Combine $s^{9}$ and $\frac{1}{2}$ .

$t^{3} \frac{s^{9}}{2} \cdot 16$

Step 5

Combine $t^{3}$ and $\frac{s^{9}}{2}$ .

$\frac{t^{3} s^{9}}{2} \cdot 16$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $16$ .

$\frac{t^{3} s^{9}}{2} \cdot (2 (8))$

Step 6.2

Cancel the common factor.

$\frac{t^{3} s^{9}}{2} \cdot (2 \cdot 8)$

Step 6.3

Rewrite the expression.

$t^{3} s^{9} \cdot 8$

Step 7

Move $8$ to the left of $t^{3} s^{9}$ .

$8 t^{3} s^{9}$