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:

\( \sqrt{\frac{81}{16}} \)
\( \frac{\sqrt{81}}{\sqrt{16}} \)
\( \frac{\sqrt{9^2}}{\sqrt{4^2}} \)
\( \frac{9}{4} \)
2\(\frac{1}{4}\)

By buying two shirts, Bob will save $48 x \( \frac{50}{100} \) = \( \frac{$48 x 50}{100} \) = \( \frac{$2400}{100} \) = $24.00 on the second shirt.

So, his total cost will be
$48.00 + ($48.00 - $24.00)
$48.00 + $24.00
$72.00

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 8 factors [1, 2, 3, 4, 6, 8, 12, 24] making 24 the greatest factor 24 and 72 have in common.

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:

-7x⁵ x 4x⁴
(-7 x 4)x^{(5 + 4)}
-28x⁹

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.