To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To add these radicals together their radicands must be the same:

4\( \sqrt{20} \) + 5\( \sqrt{5} \)
4\( \sqrt{4 \times 5} \) + 5\( \sqrt{5} \)
4\( \sqrt{2^2 \times 5} \) + 5\( \sqrt{5} \)
(4)(2)\( \sqrt{5} \) + 5\( \sqrt{5} \)
8\( \sqrt{5} \) + 5\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,500
i = 0.01 x $1,500
i = $15

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{49}} \)
\( \frac{\sqrt{4}}{\sqrt{49}} \)
\( \frac{\sqrt{2^2}}{\sqrt{7^2}} \)
\(\frac{2}{7}\)