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

8a² + 9a²
(8 + 9)a²
17a²

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:

\( \sqrt{\frac{9}{4}} \)
\( \frac{\sqrt{9}}{\sqrt{4}} \)
\( \frac{\sqrt{3^2}}{\sqrt{2^2}} \)
\( \frac{3}{2} \)
1\(\frac{1}{2}\)

By buying two shirts, Alex will save $30 x \( \frac{45}{100} \) = \( \frac{$30 x 45}{100} \) = \( \frac{$1350}{100} \) = $13.50 on the second shirt.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{16} \) = 2\(\frac{3}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 330 small cakes are needed for the party so \( \frac{330}{76} \) = 4\(\frac{13}{38}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 5 = 8 cooks.

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

\( \frac{4\sqrt{18}}{2\sqrt{9}} \)
\( \frac{4}{2} \) \( \sqrt{\frac{18}{9}} \)
2 \( \sqrt{2} \)