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:

-4z⁶ + 9z⁶
(-4 + 9)z⁶
5z⁶

The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

By buying two shirts, Frank will save $12 x \( \frac{30}{100} \) = \( \frac{$12 x 30}{100} \) = \( \frac{$360}{100} \) = $3.60 on the second shirt.

So, his total cost will be
$12.00 + ($12.00 - $3.60)
$12.00 + $8.40
$20.40

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 3}{4 x 3} \) - \( \frac{4 x 2}{6 x 2} \)

\( \frac{12}{12} \) - \( \frac{8}{12} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{12 - 8}{12} \) = \( \frac{4}{12} \) = \(\frac{1}{3}\)

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

\( \frac{40\sqrt{30}}{8\sqrt{6}} \)
\( \frac{40}{8} \) \( \sqrt{\frac{30}{6}} \)
5 \( \sqrt{5} \)