Basic Math Examples

$25^{\sqrt{2}} \cdot 125^{\sqrt{2}}$

Step 1

Rewrite $25$ as $5^{2}$ .

${(5^{2})}^{\sqrt{2}} \cdot 125^{\sqrt{2}}$

Step 2

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

$5^{2 \sqrt{2}} \cdot 125^{\sqrt{2}}$

Step 3

Rewrite $125$ as $5^{3}$ .

$5^{2 \sqrt{2}} \cdot {(5^{3})}^{\sqrt{2}}$

Step 4

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

$5^{2 \sqrt{2}} \cdot 5^{3 \sqrt{2}}$

Step 5

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

$5^{2 \sqrt{2} + 3 \sqrt{2}}$

Step 6

Add $2 \sqrt{2}$ and $3 \sqrt{2}$ .

$5^{5 \sqrt{2}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$5^{5 \sqrt{2}}$

Decimal Form:

$87591.97102943 \dots$