Basic Math Examples

(0.5 \cdot 10^{3}) (0.3 \cdot 10)

$(0.5 \cdot 10^{3}) (0.3 \cdot 10)$

Step 1

Multiply

10^{3}

$10^{3}$ by

10

$10$ by adding the exponents.

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Step 1.1

Move

10

$10$ .

0.5 \cdot 10 \cdot 10^{3} \cdot 0.3

$0.5 \cdot 10 \cdot 10^{3} \cdot 0.3$

Step 1.2

Multiply

10

$10$ by

10^{3}

$10^{3}$ .

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Step 1.2.1

Raise

10

$10$ to the power of

1

$1$ .

0.5 \cdot (10^{1} \cdot 10^{3}) \cdot 0.3

$0.5 \cdot (10^{1} \cdot 10^{3}) \cdot 0.3$

Step 1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

0.5 \cdot 10^{1 + 3} \cdot 0.3

$0.5 \cdot 10^{1 + 3} \cdot 0.3$

0.5 \cdot 10^{1 + 3} \cdot 0.3

$0.5 \cdot 10^{1 + 3} \cdot 0.3$

Step 1.3

Add

1

$1$ and

3

$3$ .

0.5 \cdot 10^{4} \cdot 0.3

$0.5 \cdot 10^{4} \cdot 0.3$

0.5 \cdot 10^{4} \cdot 0.3

$0.5 \cdot 10^{4} \cdot 0.3$

Step 2

Multiply

0.5

$0.5$ by

0.3

$0.3$ .

0.15 \cdot 10^{4}

$0.15 \cdot 10^{4}$

Step 3

Move the decimal point in

0.15

$0.15$ to the right by

1

$1$ place and decrease the power of

10^{4}

$10^{4}$ by

1

$1$ .

1.5 \cdot 10^{3}

$1.5 \cdot 10^{3}$

Step 4

The result can be shown in multiple forms.

Scientific Notation:

1.5 \cdot 10^{3}

$1.5 \cdot 10^{3}$

Expanded Form:

1500

$1500$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$