Finite Math Examples

$8 r^{3} s^{5} (7 s^{6} - 5 r + 9)$

Step 1

Apply the distributive property.

$8 r^{3} s^{5} (7 s^{6}) + 8 r^{3} s^{5} (- 5 r) + 8 r^{3} s^{5} \cdot 9$

Step 2

Simplify.

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Step 2.1

Multiply $s^{5}$ by $s^{6}$ by adding the exponents.

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Step 2.1.1

Move $s^{6}$ .

$8 r^{3} (s^{6} s^{5}) \cdot 7 + 8 r^{3} s^{5} (- 5 r) + 8 r^{3} s^{5} \cdot 9$

Step 2.1.2

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

$8 r^{3} s^{6 + 5} \cdot 7 + 8 r^{3} s^{5} (- 5 r) + 8 r^{3} s^{5} \cdot 9$

Step 2.1.3

Add $6$ and $5$ .

$8 r^{3} s^{11} \cdot 7 + 8 r^{3} s^{5} (- 5 r) + 8 r^{3} s^{5} \cdot 9$

Step 2.2

Multiply $r^{3}$ by $r$ by adding the exponents.

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Step 2.2.1

Move $r$ .

$8 r^{3} s^{11} \cdot 7 + 8 (r \cdot r^{3}) s^{5} \cdot - 5 + 8 r^{3} s^{5} \cdot 9$

Step 2.2.2

Multiply $r$ by $r^{3}$ .

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Step 2.2.2.1

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

$8 r^{3} s^{11} \cdot 7 + 8 (r^{1} r^{3}) s^{5} \cdot - 5 + 8 r^{3} s^{5} \cdot 9$

Step 2.2.2.2

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

$8 r^{3} s^{11} \cdot 7 + 8 r^{1 + 3} s^{5} \cdot - 5 + 8 r^{3} s^{5} \cdot 9$

Step 2.2.3

Add $1$ and $3$ .

$8 r^{3} s^{11} \cdot 7 + 8 r^{4} s^{5} \cdot - 5 + 8 r^{3} s^{5} \cdot 9$

Step 2.3

Multiply $9$ by $8$ .

$8 r^{3} s^{11} \cdot 7 + 8 r^{4} s^{5} \cdot - 5 + 72 r^{3} s^{5}$

Step 3

Simplify each term.

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Step 3.1

Multiply $7$ by $8$ .

$56 r^{3} s^{11} + 8 r^{4} s^{5} \cdot - 5 + 72 r^{3} s^{5}$

Step 3.2

Multiply $- 5$ by $8$ .

$56 r^{3} s^{11} - 40 r^{4} s^{5} + 72 r^{3} s^{5}$