Basic Math Examples

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

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 $- r^{5} s$ .

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

Step 1.2

Apply the product rule to $- r^{5}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $5$ by $5$ .

$- r^{25} s^{5} {(- r^{4} s^{5})}^{4}$

Step 4

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

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Step 4.1

Apply the product rule to $- r^{4} s^{5}$ .

$- r^{25} s^{5} ({(- r^{4})}^{4} {(s^{5})}^{4})$

Step 4.2

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

$- r^{25} s^{5} ({(- 1)}^{4} {(r^{4})}^{4} {(s^{5})}^{4})$

Step 5

Multiply $- 1$ by ${(- 1)}^{4}$ by adding the exponents.

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Step 5.1

Move ${(- 1)}^{4}$ .

${(- 1)}^{4} \cdot - 1 r^{25} s^{5} ({(r^{4})}^{4} {(s^{5})}^{4})$

Step 5.2

Multiply ${(- 1)}^{4}$ by $- 1$ .

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Step 5.2.1

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

${(- 1)}^{4} \cdot {(- 1)}^{1} r^{25} s^{5} ({(r^{4})}^{4} {(s^{5})}^{4})$

Step 5.2.2

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

${(- 1)}^{4 + 1} r^{25} s^{5} ({(r^{4})}^{4} {(s^{5})}^{4})$

Step 5.3

Add $4$ and $1$ .

${(- 1)}^{5} r^{25} s^{5} ({(r^{4})}^{4} {(s^{5})}^{4})$

Step 6

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

$- r^{25} s^{5} ({(r^{4})}^{4} {(s^{5})}^{4})$

Step 7

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

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Step 7.1

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

$- r^{25} s^{5} (r^{4 \cdot 4} {(s^{5})}^{4})$

Step 7.2

Multiply $4$ by $4$ .

$- r^{25} s^{5} (r^{16} {(s^{5})}^{4})$

Step 8

Multiply $r^{25}$ by $r^{16}$ by adding the exponents.

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Step 8.1

Move $r^{16}$ .

$- (r^{16} r^{25}) s^{5} {(s^{5})}^{4}$

Step 8.2

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

$- r^{16 + 25} s^{5} {(s^{5})}^{4}$

Step 8.3

Add $16$ and $25$ .

$- r^{41} s^{5} {(s^{5})}^{4}$

Step 9

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

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Step 9.1

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

$- r^{41} s^{5} s^{5 \cdot 4}$

Step 9.2

Multiply $5$ by $4$ .

$- r^{41} s^{5} s^{20}$

Step 10

Multiply $s^{5}$ by $s^{20}$ by adding the exponents.

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Step 10.1

Move $s^{20}$ .

$- r^{41} (s^{20} s^{5})$

Step 10.2

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

$- r^{41} s^{20 + 5}$

Step 10.3

Add $20$ and $5$ .

$- r^{41} s^{25}$