Basic Math Examples

${(4 r s^{4})}^{3} {(2 r^{2} s^{- 3})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $4 r s^{4}$ .

${(4 r)}^{3} {(s^{4})}^{3} {(2 r^{2} s^{- 3})}^{2}$

Step 1.2

Apply the product rule to $4 r$ .

$4^{3} r^{3} {(s^{4})}^{3} {(2 r^{2} s^{- 3})}^{2}$

Step 2

Raise $4$ to the power of $3$ .

$64 r^{3} {(s^{4})}^{3} {(2 r^{2} s^{- 3})}^{2}$

Step 3

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

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Step 3.1

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

$64 r^{3} s^{4 \cdot 3} {(2 r^{2} s^{- 3})}^{2}$

Step 3.2

Multiply $4$ by $3$ .

$64 r^{3} s^{12} {(2 r^{2} s^{- 3})}^{2}$

Step 4

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

$64 r^{3} s^{12} {(2 r^{2} \frac{1}{s^{3}})}^{2}$

Step 5

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

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Step 5.1

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

$64 r^{3} s^{12} {(r^{2} \frac{2}{s^{3}})}^{2}$

Step 5.2

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

$64 r^{3} s^{12} {(\frac{r^{2} \cdot 2}{s^{3}})}^{2}$

Step 6

Move $2$ to the left of $r^{2}$ .

$64 r^{3} s^{12} {(\frac{2 \cdot r^{2}}{s^{3}})}^{2}$

Step 7

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 7.1

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

$64 r^{3} s^{12} \frac{{(2 r^{2})}^{2}}{{(s^{3})}^{2}}$

Step 7.2

Apply the product rule to $2 r^{2}$ .

$64 r^{3} s^{12} \frac{2^{2} {(r^{2})}^{2}}{{(s^{3})}^{2}}$

Step 8

Simplify the numerator.

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Step 8.1

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

$64 r^{3} s^{12} \frac{4 {(r^{2})}^{2}}{{(s^{3})}^{2}}$

Step 8.2

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

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Step 8.2.1

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

$64 r^{3} s^{12} \frac{4 r^{2 \cdot 2}}{{(s^{3})}^{2}}$

Step 8.2.2

Multiply $2$ by $2$ .

$64 r^{3} s^{12} \frac{4 r^{4}}{{(s^{3})}^{2}}$

Step 9

Reduce the expression by cancelling the common factors.

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Step 9.1

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

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Step 9.1.1

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

$64 r^{3} s^{12} \frac{4 r^{4}}{s^{3 \cdot 2}}$

Step 9.1.2

Multiply $3$ by $2$ .

$64 r^{3} s^{12} \frac{4 r^{4}}{s^{6}}$

Step 9.2

Cancel the common factor of $s^{6}$ .

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Step 9.2.1

Factor $s^{6}$ out of $64 r^{3} s^{12}$ .

$s^{6} (64 r^{3} s^{6}) \frac{4 r^{4}}{s^{6}}$

Step 9.2.2

Cancel the common factor.

$s^{6} (64 r^{3} s^{6}) \frac{4 r^{4}}{s^{6}}$

Step 9.2.3

Rewrite the expression.

$64 r^{3} s^{6} (4 r^{4})$

Step 9.3

Multiply $4$ by $64$ .

$256 r^{3} s^{6} r^{4}$

Step 10

Multiply $r^{3}$ by $r^{4}$ by adding the exponents.

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Step 10.1

Move $r^{4}$ .

$256 (r^{4} r^{3}) s^{6}$

Step 10.2

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

$256 r^{4 + 3} s^{6}$

Step 10.3

Add $4$ and $3$ .

$256 r^{7} s^{6}$