Basic Math Examples

$- 8^{5} - 5 y^{3} + 7 y^{2} - 9 + 2 y^{5} \cdot 10^{3} \cdot (8 y) + 5$

Step 1

Simplify each term.

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Step 1.1

Raise $8$ to the power of $5$ .

$- 1 \cdot 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 y^{5} \cdot 10^{3} \cdot (8 y) + 5$

Step 1.2

Multiply $- 1$ by $32768$ .

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 y^{5} \cdot 10^{3} \cdot (8 y) + 5$

Step 1.3

Multiply $y^{5}$ by $y$ by adding the exponents.

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Step 1.3.1

Move $y$ .

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 (y \cdot y^{5}) \cdot 10^{3} \cdot 8 + 5$

Step 1.3.2

Multiply $y$ by $y^{5}$ .

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Step 1.3.2.1

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

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 (y^{1} y^{5}) \cdot 10^{3} \cdot 8 + 5$

Step 1.3.2.2

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

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 y^{1 + 5} \cdot 10^{3} \cdot 8 + 5$

Step 1.3.3

Add $1$ and $5$ .

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 y^{6} \cdot 10^{3} \cdot 8 + 5$

Step 1.4

Raise $10$ to the power of $3$ .

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2 y^{6} \cdot 1000 \cdot 8 + 5$

Step 1.5

Multiply $1000$ by $2$ .

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 2000 y^{6} \cdot 8 + 5$

Step 1.6

Multiply $8$ by $2000$ .

$- 32768 - 5 y^{3} + 7 y^{2} - 9 + 16000 y^{6} + 5$

Step 2

Simplify the expression.

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Step 2.1

Subtract $9$ from $- 32768$ .

$- 5 y^{3} + 7 y^{2} - 32777 + 16000 y^{6} + 5$

Step 2.2

Add $- 32777$ and $5$ .

$- 5 y^{3} + 7 y^{2} + 16000 y^{6} - 32772$

Step 2.3

Move $7 y^{2}$ .

$- 5 y^{3} + 16000 y^{6} + 7 y^{2} - 32772$

Step 2.4

Reorder $- 5 y^{3}$ and $16000 y^{6}$ .

$16000 y^{6} - 5 y^{3} + 7 y^{2} - 32772$