Basic Math Examples

$\frac{3^{10} \cdot 3^{3}}{3 \cdot 3^{- 5}}$

Step 1

Multiply $3^{10}$ by $3^{3}$ by adding the exponents.

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Step 1.1

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

$\frac{3^{10 + 3}}{3 \cdot 3^{- 5}}$

Step 1.2

Add $10$ and $3$ .

$\frac{3^{13}}{3 \cdot 3^{- 5}}$

Step 2

Multiply $3$ by $3^{- 5}$ by adding the exponents.

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Step 2.1

Multiply $3$ by $3^{- 5}$ .

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Step 2.1.1

Raise $3$ to the power of $1$ .

$\frac{3^{13}}{3^{1} \cdot 3^{- 5}}$

Step 2.1.2

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

$\frac{3^{13}}{3^{1 - 5}}$

Step 2.2

Subtract $5$ from $1$ .

$\frac{3^{13}}{3^{- 4}}$

Step 3

Move $3^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3^{13} \cdot 3^{4}$

Step 4

Multiply $3^{13}$ by $3^{4}$ by adding the exponents.

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Step 4.1

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

$3^{13 + 4}$

Step 4.2

Add $13$ and $4$ .

$3^{17}$

Step 5

Raise $3$ to the power of $17$ .

$129140163$