Basic Math Examples

$\frac{{(3^{7} \cdot 3^{- 3})}^{- 5}}{3^{9}}$

Step 1

Move ${(3^{7} \cdot 3^{- 3})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{9} {(3^{7} \cdot 3^{- 3})}^{5}}$

Step 2

Multiply $3^{7}$ by $3^{- 3}$ by adding the exponents.

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Step 2.1

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

$\frac{1}{3^{9} {(3^{7 - 3})}^{5}}$

Step 2.2

Subtract $3$ from $7$ .

$\frac{1}{3^{9} {(3^{4})}^{5}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $3$ to the power of $9$ .

$\frac{1}{19683 {(3^{4})}^{5}}$

Step 3.2

Multiply the exponents in ${(3^{4})}^{5}$ .

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Step 3.2.1

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

$\frac{1}{19683 \cdot 3^{4 \cdot 5}}$

Step 3.2.2

Multiply $4$ by $5$ .

$\frac{1}{19683 \cdot 3^{20}}$

Step 3.3

Raise $3$ to the power of $20$ .

$\frac{1}{19683 \cdot 3486784401}$

Step 4

Multiply $19683$ by $3486784401$ .

$\frac{1}{68630377364883}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{68630377364883}$

Decimal Form:

$1.45708072 \cdot 10^{- 14}$