Basic Math Examples

${(a^{15} \div a^{3})}^{2} \cdot a^{5}$

Step 1

Rewrite the division as a fraction.

${(\frac{a^{15}}{a^{3}})}^{2} \cdot a^{5}$

Step 2

Cancel the common factor of $a^{15}$ and $a^{3}$ .

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Step 2.1

Factor $a^{3}$ out of $a^{15}$ .

${(\frac{a^{3} a^{12}}{a^{3}})}^{2} \cdot a^{5}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

${(\frac{a^{3} a^{12}}{a^{3} \cdot 1})}^{2} \cdot a^{5}$

Step 2.2.2

Cancel the common factor.

${(\frac{a^{3} a^{12}}{a^{3} \cdot 1})}^{2} \cdot a^{5}$

Step 2.2.3

Rewrite the expression.

${(\frac{a^{12}}{1})}^{2} \cdot a^{5}$

Step 2.2.4

Divide $a^{12}$ by $1$ .

${(a^{12})}^{2} \cdot a^{5}$

Step 3

Multiply the exponents in ${(a^{12})}^{2}$ .

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Step 3.1

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

$a^{12 \cdot 2} \cdot a^{5}$

Step 3.2

Multiply $12$ by $2$ .

$a^{24} \cdot a^{5}$

Step 4

Multiply $a^{24}$ by $a^{5}$ by adding the exponents.

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Step 4.1

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

$a^{24 + 5}$

Step 4.2

Add $24$ and $5$ .

$a^{29}$