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:

-5a² x 9a³
(-5 x 9)a^{(2 + 3)}
-45a⁵

The equation for this sequence is:

a_n = a_n-1 + 7

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 + 7
a₆ = 29 + 7
a₆ = 36

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{70}{100} \) = \( \frac{70 x 25}{100} \) = \( \frac{1750}{100} \) = 17 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{17}{\frac{50}{100}} \) = 17 x \( \frac{100}{50} \) = \( \frac{17 x 100}{50} \) = \( \frac{1700}{50} \) = 34 shots

to make the same number of shots as the guard and thus score the same number of points.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

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

7\( \sqrt{45} \) + 9\( \sqrt{5} \)
7\( \sqrt{9 \times 5} \) + 9\( \sqrt{5} \)
7\( \sqrt{3^2 \times 5} \) + 9\( \sqrt{5} \)
(7)(3)\( \sqrt{5} \) + 9\( \sqrt{5} \)
21\( \sqrt{5} \) + 9\( \sqrt{5} \)

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