Basic Math Examples

$a^{5} r^{10} = 2^{15}$

Step 1

Divide each term in $a^{5} r^{10} = 2^{15}$ by $r^{10}$ and simplify.

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Step 1.1

Divide each term in $a^{5} r^{10} = 2^{15}$ by $r^{10}$ .

$\frac{a^{5} r^{10}}{r^{10}} = \frac{2^{15}}{r^{10}}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $r^{10}$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{a^{5} r^{10}}{r^{10}} = \frac{2^{15}}{r^{10}}$

Step 1.2.1.2

Divide $a^{5}$ by $1$ .

$a^{5} = \frac{2^{15}}{r^{10}}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Raise $2$ to the power of $15$ .

$a^{5} = \frac{32768}{r^{10}}$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \sqrt[5]{\frac{32768}{r^{10}}}$

Step 3

Simplify $\sqrt[5]{\frac{32768}{r^{10}}}$ .

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Step 3.1

Rewrite $32768$ as $8^{5}$ .

$a = \sqrt[5]{\frac{8^{5}}{r^{10}}}$

Step 3.2

Rewrite $r^{10}$ as ${(r^{2})}^{5}$ .

$a = \sqrt[5]{\frac{8^{5}}{{(r^{2})}^{5}}}$

Step 3.3

Rewrite $\frac{8^{5}}{{(r^{2})}^{5}}$ as ${(\frac{8}{r^{2}})}^{5}$ .

$a = \sqrt[5]{{(\frac{8}{r^{2}})}^{5}}$

Step 3.4

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

$a = \frac{8}{r^{2}}$