Basic Math Examples

$\sqrt{\sqrt[3]{a^{12}}} - {(a^{16} \div a^{15})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $a^{12}$ as ${(a^{4})}^{3}$ .

$\sqrt{\sqrt[3]{{(a^{4})}^{3}}} - {(a^{16} \div a^{15})}^{2}$

Step 1.2

Pull terms out from under the radical, assuming real numbers.

$\sqrt{a^{4}} - {(a^{16} \div a^{15})}^{2}$

Step 1.3

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{{(a^{2})}^{2}} - {(a^{16} \div a^{15})}^{2}$

Step 1.4

Pull terms out from under the radical, assuming positive real numbers.

$a^{2} - {(a^{16} \div a^{15})}^{2}$

Step 1.5

Rewrite the division as a fraction.

$a^{2} - {(\frac{a^{16}}{a^{15}})}^{2}$

Step 1.6

Cancel the common factor of $a^{16}$ and $a^{15}$ .

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Step 1.6.1

Factor $a^{15}$ out of $a^{16}$ .

$a^{2} - {(\frac{a^{15} a}{a^{15}})}^{2}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Multiply by $1$ .

$a^{2} - {(\frac{a^{15} a}{a^{15} \cdot 1})}^{2}$

Step 1.6.2.2

Cancel the common factor.

$a^{2} - {(\frac{a^{15} a}{a^{15} \cdot 1})}^{2}$

Step 1.6.2.3

Rewrite the expression.

$a^{2} - {(\frac{a}{1})}^{2}$

Step 1.6.2.4

Divide $a$ by $1$ .

$a^{2} - a^{2}$

Step 2

Subtract $a^{2}$ from $a^{2}$ .

$0$