Algebra Examples

${(r^{- 2} s^{3})}^{2} {(3 s)}^{2}$

Step 1

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

${(\frac{1}{r^{2}} s^{3})}^{2} {(3 s)}^{2}$

Step 2

Combine $\frac{1}{r^{2}}$ and $s^{3}$ .

${(\frac{s^{3}}{r^{2}})}^{2} {(3 s)}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{s^{3}}{r^{2}}$ .

$\frac{{(s^{3})}^{2}}{{(r^{2})}^{2}} {(3 s)}^{2}$

Step 3.2

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

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Step 3.2.1

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

$\frac{s^{3 \cdot 2}}{{(r^{2})}^{2}} {(3 s)}^{2}$

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{s^{6}}{{(r^{2})}^{2}} {(3 s)}^{2}$

Step 3.3

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

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Step 3.3.1

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

$\frac{s^{6}}{r^{2 \cdot 2}} {(3 s)}^{2}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{s^{6}}{r^{4}} {(3 s)}^{2}$

Step 3.4

Apply the product rule to $3 s$ .

$\frac{s^{6}}{r^{4}} (3^{2} s^{2})$

Step 3.5

Rewrite using the commutative property of multiplication.

$3^{2} \frac{s^{6}}{r^{4}} s^{2}$

Step 3.6

Raise $3$ to the power of $2$ .

$9 \frac{s^{6}}{r^{4}} s^{2}$

Step 4

Combine $9$ and $\frac{s^{6}}{r^{4}}$ .

$\frac{9 s^{6}}{r^{4}} s^{2}$

Step 5

Multiply $\frac{9 s^{6}}{r^{4}} s^{2}$ .

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Step 5.1

Combine $\frac{9 s^{6}}{r^{4}}$ and $s^{2}$ .

$\frac{9 s^{6} s^{2}}{r^{4}}$

Step 5.2

Multiply $s^{6}$ by $s^{2}$ by adding the exponents.

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Step 5.2.1

Move $s^{2}$ .

$\frac{9 (s^{2} s^{6})}{r^{4}}$

Step 5.2.2

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

$\frac{9 s^{2 + 6}}{r^{4}}$

Step 5.2.3

Add $2$ and $6$ .

$\frac{9 s^{8}}{r^{4}}$