Basic Math Examples

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

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

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

$16000 y^{6}$ .

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