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

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

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

\( \frac{5 x 5}{2 x 5} \) - \( \frac{6 x 1}{10 x 1} \)

\( \frac{25}{10} \) - \( \frac{6}{10} \)

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

\( \frac{25 - 6}{10} \) = \( \frac{19}{10} \) = 1\(\frac{9}{10}\)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

By buying two shirts, Charlie will save $30 x \( \frac{30}{100} \) = \( \frac{$30 x 30}{100} \) = \( \frac{$900}{100} \) = $9.00 on the second shirt.

So, his total cost will be
$30.00 + ($30.00 - $9.00)
$30.00 + $21.00
$51.00