Pre-Algebra Examples

$3^{2 r} \cdot {(3 a)}^{r} \cdot {(3^{- 3})}^{r}$

Step 1

Apply the product rule to $3 a$ .

$3^{2 r} \cdot (3^{r} a^{r}) \cdot {(3^{- 3})}^{r}$

Step 2

Multiply $3^{2 r}$ by $3^{r}$ by adding the exponents.

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Step 2.1

Move $3^{r}$ .

$3^{r} \cdot 3^{2 r} \cdot a^{r} \cdot {(3^{- 3})}^{r}$

Step 2.2

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

$3^{r + 2 r} \cdot a^{r} \cdot {(3^{- 3})}^{r}$

Step 2.3

Add $r$ and $2 r$ .

$3^{3 r} \cdot a^{r} \cdot {(3^{- 3})}^{r}$

Step 3

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

$3^{3 r} a^{r} \cdot {(\frac{1}{3^{3}})}^{r}$

Step 4

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

$3^{3 r} a^{r} \cdot {(\frac{1}{27})}^{r}$

Step 5

Apply the product rule to $\frac{1}{27}$ .

$3^{3 r} a^{r} \cdot \frac{1^{r}}{27^{r}}$

Step 6

One to any power is one.

$3^{3 r} a^{r} \cdot \frac{1}{27^{r}}$

Step 7

Multiply $3^{3 r} a^{r} \frac{1}{27^{r}}$ .

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Step 7.1

Combine $3^{3 r}$ and $\frac{1}{27^{r}}$ .

$a^{r} \frac{3^{3 r}}{27^{r}}$

Step 7.2

Combine $a^{r}$ and $\frac{3^{3 r}}{27^{r}}$ .

$\frac{a^{r} \cdot 3^{3 r}}{27^{r}}$