Basic Math Examples

$27 \cdot 243^{- 3 k}$

Step 1

Rewrite $27$ as $3^{3}$ .

$3^{3} \cdot 243^{- 3 k}$

Step 2

Rewrite $243$ as $3^{5}$ .

$3^{3} \cdot {(3^{5})}^{- 3 k}$

Step 3

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

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Step 3.1

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

$3^{3} \cdot 3^{5 (- 3 k)}$

Step 3.2

Multiply $- 3$ by $5$ .

$3^{3} \cdot 3^{- 15 k}$

Step 4

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

$3^{3 - 15 k}$