To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

5b³ x 8b⁶
(5 x 8)b^{(3 + 6)}
40b⁹

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 $800
i = 0.07 x $800

No payments were made so the total amount due is the original amount + the accumulated interest:

If 68% of the town's 21,000 voters cast ballots the number of votes cast is:

(\( \frac{68}{100} \)) x 21,000 = \( \frac{1,428,000}{100} \) = 14,280

The mayor got 84% of the votes cast which is:

(\( \frac{84}{100} \)) x 14,280 = \( \frac{1,199,520}{100} \) = 11,995 votes.

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:

\( \sqrt{\frac{25}{49}} \)
\( \frac{\sqrt{25}}{\sqrt{49}} \)
\( \frac{\sqrt{5^2}}{\sqrt{7^2}} \)
\(\frac{5}{7}\)

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. 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 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.