Basic Math Examples

${(3^{5})}^{2} {(3^{- 4})}^{5}$

Step 1

Multiply the exponents in ${(3^{5})}^{2}$ .

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Step 1.1

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

$3^{5 \cdot 2} {(3^{- 4})}^{5}$

Step 1.2

Multiply $5$ by $2$ .

$3^{10} {(3^{- 4})}^{5}$

Step 2

Raise $3$ to the power of $10$ .

$59049 {(3^{- 4})}^{5}$

Step 3

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

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Step 3.1

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

$59049 \cdot 3^{- 4 \cdot 5}$

Step 3.2

Multiply $- 4$ by $5$ .

$59049 \cdot 3^{- 20}$

Step 4

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

$59049 \cdot \frac{1}{3^{20}}$

Step 5

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

$59049 \cdot \frac{1}{3486784401}$

Step 6

Cancel the common factor of $59049$ .

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Step 6.1

Factor $59049$ out of $3486784401$ .

$59049 \cdot \frac{1}{59049 (59049)}$

Step 6.2

Cancel the common factor.

$59049 \cdot \frac{1}{59049 \cdot 59049}$

Step 6.3

Rewrite the expression.

$\frac{1}{59049}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{59049}$

Decimal Form:

$1.69350878 \cdot 10^{- 5}$