Basic Math Examples

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

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 $- r^{3} s$ .

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

Step 1.2

Apply the product rule to $- r^{3}$ .

${(- 1)}^{2} {(r^{3})}^{2} s^{2} {(- r^{4} s^{3})}^{5}$

Step 2

Raise $- 1$ to the power of $2$ .

$1 {(r^{3})}^{2} s^{2} {(- r^{4} s^{3})}^{5}$

Step 3

Multiply ${(r^{3})}^{2}$ by $1$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $2$ .

$r^{6} s^{2} {(- r^{4} s^{3})}^{5}$

Step 5

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

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Step 5.1

Apply the product rule to $- r^{4} s^{3}$ .

$r^{6} s^{2} ({(- r^{4})}^{5} {(s^{3})}^{5})$

Step 5.2

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

$r^{6} s^{2} ({(- 1)}^{5} {(r^{4})}^{5} {(s^{3})}^{5})$

Step 6

Rewrite using the commutative property of multiplication.

${(- 1)}^{5} r^{6} s^{2} ({(r^{4})}^{5} {(s^{3})}^{5})$

Step 7

Raise $- 1$ to the power of $5$ .

$- r^{6} s^{2} ({(r^{4})}^{5} {(s^{3})}^{5})$

Step 8

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

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Step 8.1

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

$- r^{6} s^{2} (r^{4 \cdot 5} {(s^{3})}^{5})$

Step 8.2

Multiply $4$ by $5$ .

$- r^{6} s^{2} (r^{20} {(s^{3})}^{5})$

Step 9

Multiply $r^{6}$ by $r^{20}$ by adding the exponents.

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Step 9.1

Move $r^{20}$ .

$- (r^{20} r^{6}) s^{2} {(s^{3})}^{5}$

Step 9.2

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

$- r^{20 + 6} s^{2} {(s^{3})}^{5}$

Step 9.3

Add $20$ and $6$ .

$- r^{26} s^{2} {(s^{3})}^{5}$

Step 10

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

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Step 10.1

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

$- r^{26} s^{2} s^{3 \cdot 5}$

Step 10.2

Multiply $3$ by $5$ .

$- r^{26} s^{2} s^{15}$

Step 11

Multiply $s^{2}$ by $s^{15}$ by adding the exponents.

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Step 11.1

Move $s^{15}$ .

$- r^{26} (s^{15} s^{2})$

Step 11.2

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

$- r^{26} s^{15 + 2}$

Step 11.3

Add $15$ and $2$ .

$- r^{26} s^{17}$