Algebra Examples

$A (t) = p {(1 + \frac{r}{n})}^{n t}$

Step 1

Divide each term in $A t = p {(1 + \frac{r}{n})}^{n t}$ by $t$ .

$\frac{A t}{t} = \frac{p {(1 + \frac{r}{n})}^{n t}}{t}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $t$ .

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Step 2.1.1

Cancel the common factor.

$\frac{A t}{t} = \frac{p {(1 + \frac{r}{n})}^{n t}}{t}$

Step 2.1.2

Divide $A$ by $1$ .

$A = \frac{p {(1 + \frac{r}{n})}^{n t}}{t}$

Step 3

Simplify the right side.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Write $1$ as a fraction with a common denominator.

$A = \frac{p {(\frac{n}{n} + \frac{r}{n})}^{n t}}{t}$

Step 3.1.2

Combine the numerators over the common denominator.

$A = \frac{p {(\frac{n + r}{n})}^{n t}}{t}$

Step 3.1.3

Apply the product rule to $\frac{n + r}{n}$ .

$A = \frac{p \frac{{(n + r)}^{n t}}{n^{n t}}}{t}$

Step 3.2

Combine $p$ and $\frac{{(n + r)}^{n t}}{n^{n t}}$ .

$A = \frac{\frac{p {(n + r)}^{n t}}{n^{n t}}}{t}$

Step 3.3

Multiply the numerator by the reciprocal of the denominator.

$A = \frac{p {(n + r)}^{n t}}{n^{n t}} \cdot \frac{1}{t}$

Step 3.4

Combine.

$A = \frac{p {(n + r)}^{n t} \cdot 1}{n^{n t} t}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Multiply $p$ by $1$ .

$A = \frac{p {(n + r)}^{n t}}{n^{n t} t}$

Step 3.5.2

Reorder factors in $\frac{p {(n + r)}^{n t}}{n^{n t} t}$ .

$A = \frac{p {(n + r)}^{n t}}{t n^{n t}}$