Finite Math Examples

$\frac{2 \sqrt{9^{5}} + 7 \sqrt{9^{5}}}{\sqrt{9^{7}}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $9$ to the power of $5$ .

$\frac{2 \sqrt{59049} + 7 \sqrt{9^{5}}}{\sqrt{9^{7}}}$

Step 1.2

Rewrite $59049$ as $243^{2}$ .

$\frac{2 \sqrt{243^{2}} + 7 \sqrt{9^{5}}}{\sqrt{9^{7}}}$

Step 1.3

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

$\frac{2 \cdot 243 + 7 \sqrt{9^{5}}}{\sqrt{9^{7}}}$

Step 1.4

Multiply $2$ by $243$ .

$\frac{486 + 7 \sqrt{9^{5}}}{\sqrt{9^{7}}}$

Step 1.5

Raise $9$ to the power of $5$ .

$\frac{486 + 7 \sqrt{59049}}{\sqrt{9^{7}}}$

Step 1.6

Rewrite $59049$ as $243^{2}$ .

$\frac{486 + 7 \sqrt{243^{2}}}{\sqrt{9^{7}}}$

Step 1.7

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

$\frac{486 + 7 \cdot 243}{\sqrt{9^{7}}}$

Step 1.8

Multiply $7$ by $243$ .

$\frac{486 + 1701}{\sqrt{9^{7}}}$

Step 1.9

Add $486$ and $1701$ .

$\frac{2187}{\sqrt{9^{7}}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $9$ to the power of $7$ .

$\frac{2187}{\sqrt{4782969}}$

Step 2.2

Rewrite $4782969$ as $2187^{2}$ .

$\frac{2187}{\sqrt{2187^{2}}}$

Step 2.3

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

$\frac{2187}{2187}$

Step 3

Divide $2187$ by $2187$ .

$1$