Basic Math Examples

$\frac{3^{n + 1}}{5^{n + 1}} \cdot \frac{5^{n}}{3^{n}}$

Step 1

Simplify terms.

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Step 1.1

Combine.

$\frac{3^{n + 1} \cdot 5^{n}}{5^{n + 1} \cdot 3^{n}}$

Step 1.2

Cancel the common factor of $3^{n + 1}$ and $3^{n}$ .

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Step 1.2.1

Factor $3^{n}$ out of $3^{n + 1} \cdot 5^{n}$ .

$\frac{3^{n} (3 \cdot 5^{n})}{5^{n + 1} \cdot 3^{n}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3^{n}$ out of $5^{n + 1} \cdot 3^{n}$ .

$\frac{3^{n} (3 \cdot 5^{n})}{3^{n} \cdot 5^{n + 1}}$

Step 1.2.2.2

Cancel the common factor.

$\frac{3^{n} (3 \cdot 5^{n})}{3^{n} \cdot 5^{n + 1}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{3 \cdot 5^{n}}{5^{n + 1}}$

Step 1.3

Cancel the common factor of $5^{n}$ and $5^{n + 1}$ .

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Step 1.3.1

Factor $5^{n + 1}$ out of $3 \cdot 5^{n}$ .

$\frac{5^{n + 1} (3 \cdot 5^{n - (n + 1)})}{5^{n + 1}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Multiply by $1$ .

$\frac{5^{n + 1} (3 \cdot 5^{n - (n + 1)})}{5^{n + 1} \cdot 1}$

Step 1.3.2.2

Cancel the common factor.

$\frac{5^{n + 1} (3 \cdot 5^{n - (n + 1)})}{5^{n + 1} \cdot 1}$

Step 1.3.2.3

Rewrite the expression.

$\frac{3 \cdot 5^{n - (n + 1)}}{1}$

Step 1.3.2.4

Divide $3 \cdot 5^{n - (n + 1)}$ by $1$ .

$3 \cdot 5^{n - (n + 1)}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$3 \cdot 5^{n - n - 1 \cdot 1}$

Step 2.2

Multiply $- 1$ by $1$ .

$3 \cdot 5^{n - n - 1}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $n$ from $n$ .

$3 \cdot 5^{0 - 1}$

Step 3.2

Subtract $1$ from $0$ .

$3 \cdot 5^{- 1}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 \cdot \frac{1}{5}$

Step 5

Combine $3$ and $\frac{1}{5}$ .

$\frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$