To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{7} \) x \( \frac{3}{5} \) = \( \frac{4 x 3}{7 x 5} \) = \( \frac{12}{35} \) = \(\frac{12}{35}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

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

\( \frac{7 x 2}{8 x 2} \) - \( \frac{2 x 1}{16 x 1} \)

\( \frac{14}{16} \) - \( \frac{2}{16} \)

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

\( \frac{14 - 2}{16} \) = \( \frac{12}{16} \) = \(\frac{3}{4}\)

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

3\( \sqrt{18} \) - 7\( \sqrt{2} \)
3\( \sqrt{9 \times 2} \) - 7\( \sqrt{2} \)
3\( \sqrt{3^2 \times 2} \) - 7\( \sqrt{2} \)
(3)(3)\( \sqrt{2} \) - 7\( \sqrt{2} \)
9\( \sqrt{2} \) - 7\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

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

-4b⁴ - 6b⁴
(-4 - 6)b⁴
-10b⁴

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (4 + 2) ÷ 5 x 5 - 5²
P: 5 + (6) ÷ 5 x 5 - 5²
E: 5 + 6 ÷ 5 x 5 - 25
MD: 5 + \( \frac{6}{5} \) x 5 - 25
MD: 5 + \( \frac{30}{5} \) - 25
AS: \( \frac{25}{5} \) + \( \frac{30}{5} \) - 25
AS: \( \frac{55}{5} \) - 25
AS: \( \frac{55 - 125}{5} \)
\( \frac{-70}{5} \)
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