To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-1b³ - 7b³
(-1 - 7)b³
-8b³

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{16\sqrt{10}}{8\sqrt{2}} \)
\( \frac{16}{8} \) \( \sqrt{\frac{10}{2}} \)
2 \( \sqrt{5} \)

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 $200
i = 0.05 x $200
i = $10

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{52} \) = \( \frac{\frac{32}{4}}{\frac{52}{4}} \) = \( \frac{8}{13} \)

The equation for this sequence is:

a_n = a_n-1 + 1

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 1
a₆ = 5 + 1
a₆ = 6