Basic Math Examples

$\frac{1}{2} \cdot \frac{(\frac{1}{\sqrt{3 c^{2} + y^{2}}}) (10 c) (d c)}{d t}$

Step 1

Combine.

$\frac{1 ((\frac{1}{\sqrt{3 c^{2} + y^{2}}}) (10 c) (d c))}{2 (d t)}$

Step 2

Multiply $c$ by $c$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $c$ .

$\frac{1 (\frac{1}{\sqrt{3 c^{2} + y^{2}}} (10 (c \cdot c)) d)}{2 (d t)}$

Step 2.2

Multiply $c$ by $c$ .

$\frac{1 (\frac{1}{\sqrt{3 c^{2} + y^{2}}} (10 c^{2}) d)}{2 (d t)}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Multiply $\frac{1}{\sqrt{3 c^{2} + y^{2}}} (10 c^{2}) d$ by $1$ .

$\frac{\frac{1}{\sqrt{3 c^{2} + y^{2}}} (10 c^{2}) d}{2 (d t)}$

Step 3.2

Cancel the common factor of $10$ and $2$ .

Tap for more steps...

Step 3.2.1

Factor $2$ out of $\frac{1}{\sqrt{3 c^{2} + y^{2}}} (10 c^{2}) d$ .

$\frac{2 (\frac{1}{\sqrt{3 c^{2} + y^{2}}} (5 c^{2}) d)}{2 (d t)}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor.

$\frac{2 (\frac{1}{\sqrt{3 c^{2} + y^{2}}} (5 c^{2}) d)}{2 (d t)}$

Step 3.2.2.2

Rewrite the expression.

$\frac{\frac{1}{\sqrt{3 c^{2} + y^{2}}} (5 c^{2}) d}{d t}$

Step 3.3

Cancel the common factor of $d$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

$\frac{\frac{1}{\sqrt{3 c^{2} + y^{2}}} (5 c^{2}) d}{d t}$

Step 3.3.2

Rewrite the expression.

$\frac{\frac{1}{\sqrt{3 c^{2} + y^{2}}} (5 c^{2})}{t}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Combine $5$ and $\frac{1}{\sqrt{3 c^{2} + y^{2}}}$ .

$\frac{\frac{5}{\sqrt{3 c^{2} + y^{2}}} c^{2}}{t}$

Step 4.2

Combine $\frac{5}{\sqrt{3 c^{2} + y^{2}}}$ and $c^{2}$ .

$\frac{\frac{5 c^{2}}{\sqrt{3 c^{2} + y^{2}}}}{t}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $\frac{5 c^{2}}{\sqrt{3 c^{2} + y^{2}}}$ by $\frac{\sqrt{3 c^{2} + y^{2}}}{\sqrt{3 c^{2} + y^{2}}}$ .

$\frac{\frac{5 c^{2}}{\sqrt{3 c^{2} + y^{2}}} \cdot \frac{\sqrt{3 c^{2} + y^{2}}}{\sqrt{3 c^{2} + y^{2}}}}{t}$

Step 5.2

Combine and simplify the denominator.

Tap for more steps...

Step 5.2.1

Multiply $\frac{5 c^{2}}{\sqrt{3 c^{2} + y^{2}}}$ by $\frac{\sqrt{3 c^{2} + y^{2}}}{\sqrt{3 c^{2} + y^{2}}}$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{\sqrt{3 c^{2} + y^{2}} \sqrt{3 c^{2} + y^{2}}}}{t}$

Step 5.2.2

Raise $\sqrt{3 c^{2} + y^{2}}$ to the power of $1$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{\sqrt{3 c^{2} + y^{2}}}^{1} \sqrt{3 c^{2} + y^{2}}}}{t}$

Step 5.2.3

Raise $\sqrt{3 c^{2} + y^{2}}$ to the power of $1$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{\sqrt{3 c^{2} + y^{2}}}^{1} {\sqrt{3 c^{2} + y^{2}}}^{1}}}{t}$

Step 5.2.4

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

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{\sqrt{3 c^{2} + y^{2}}}^{1 + 1}}}{t}$

Step 5.2.5

Add $1$ and $1$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{\sqrt{3 c^{2} + y^{2}}}^{2}}}{t}$

Step 5.2.6

Rewrite ${\sqrt{3 c^{2} + y^{2}}}^{2}$ as $3 c^{2} + y^{2}$ .

Tap for more steps...

Step 5.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 c^{2} + y^{2}}$ as ${(3 c^{2} + y^{2})}^{\frac{1}{2}}$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{({(3 c^{2} + y^{2})}^{\frac{1}{2}})}^{2}}}{t}$

Step 5.2.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{(3 c^{2} + y^{2})}^{\frac{1}{2} \cdot 2}}}{t}$

Step 5.2.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{(3 c^{2} + y^{2})}^{\frac{2}{2}}}}{t}$

Step 5.2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.6.4.1

Cancel the common factor.

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{(3 c^{2} + y^{2})}^{\frac{2}{2}}}}{t}$

Step 5.2.6.4.2

Rewrite the expression.

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{{(3 c^{2} + y^{2})}^{1}}}{t}$

Step 5.2.6.5

Simplify.

$\frac{\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{3 c^{2} + y^{2}}}{t}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{3 c^{2} + y^{2}} \cdot \frac{1}{t}$

Step 7

Multiply $\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{3 c^{2} + y^{2}}$ by $\frac{1}{t}$ .

$\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{(3 c^{2} + y^{2}) t}$

Step 8

Reorder factors in $\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{(3 c^{2} + y^{2}) t}$ .

$\frac{5 c^{2} \sqrt{3 c^{2} + y^{2}}}{t (3 c^{2} + y^{2})}$