Basic Math Examples

${(a + 5)}^{9} {(a + 5)}^{- 5}$

Step 1

Multiply ${(a + 5)}^{9}$ by ${(a + 5)}^{- 5}$ by adding the exponents.

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Step 1.1

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

${(a + 5)}^{9 - 5}$

Step 1.2

Subtract $5$ from $9$ .

${(a + 5)}^{4}$

Step 2

Use the Binomial Theorem.

$a^{4} + 4 a^{3} \cdot 5 + 6 a^{2} \cdot 5^{2} + 4 a \cdot 5^{3} + 5^{4}$

Step 3

Simplify each term.

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Step 3.1

Multiply $5$ by $4$ .

$a^{4} + 20 a^{3} + 6 a^{2} \cdot 5^{2} + 4 a \cdot 5^{3} + 5^{4}$

Step 3.2

Raise $5$ to the power of $2$ .

$a^{4} + 20 a^{3} + 6 a^{2} \cdot 25 + 4 a \cdot 5^{3} + 5^{4}$

Step 3.3

Multiply $25$ by $6$ .

$a^{4} + 20 a^{3} + 150 a^{2} + 4 a \cdot 5^{3} + 5^{4}$

Step 3.4

Raise $5$ to the power of $3$ .

$a^{4} + 20 a^{3} + 150 a^{2} + 4 a \cdot 125 + 5^{4}$

Step 3.5

Multiply $125$ by $4$ .

$a^{4} + 20 a^{3} + 150 a^{2} + 500 a + 5^{4}$

Step 3.6

Raise $5$ to the power of $4$ .

$a^{4} + 20 a^{3} + 150 a^{2} + 500 a + 625$