Algebra Examples

$\frac{5 {(5)}^{2} - 1}{5^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $5$ by $5^{2}$ by adding the exponents.

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Step 1.1.1

Multiply $5$ by $5^{2}$ .

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Step 1.1.1.1

Raise $5$ to the power of $1$ .

$\frac{5^{1} \cdot 5^{2} - 1}{5^{2}}$

Step 1.1.1.2

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

$\frac{5^{1 + 2} - 1}{5^{2}}$

Step 1.1.2

Add $1$ and $2$ .

$\frac{5^{3} - 1}{5^{2}}$

Step 1.2

Raise $5$ to the power of $3$ .

$\frac{125 - 1}{5^{2}}$

Step 1.3

Subtract $1$ from $125$ .

$\frac{124}{5^{2}}$

Step 2

Raise $5$ to the power of $2$ .

$\frac{124}{25}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{124}{25}$

Decimal Form:

$4.96$

Mixed Number Form:

$4 \frac{24}{25}$