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.

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:

\( \sqrt{\frac{64}{36}} \)
\( \frac{\sqrt{64}}{\sqrt{36}} \)
\( \frac{\sqrt{8^2}}{\sqrt{6^2}} \)
\( \frac{8}{6} \)
1\(\frac{1}{3}\)

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{5 x 4}{2 x 4} \) - \( \frac{2 x 1}{8 x 1} \)

\( \frac{20}{8} \) - \( \frac{2}{8} \)

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

\( \frac{20 - 2}{8} \) = \( \frac{18}{8} \) = 2\(\frac{1}{4}\)

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

4 + (3 + 4) ÷ 4 x 5 - 3²
P: 4 + (7) ÷ 4 x 5 - 3²
E: 4 + 7 ÷ 4 x 5 - 9
MD: 4 + \( \frac{7}{4} \) x 5 - 9
MD: 4 + \( \frac{35}{4} \) - 9
AS: \( \frac{16}{4} \) + \( \frac{35}{4} \) - 9
AS: \( \frac{51}{4} \) - 9
AS: \( \frac{51 - 36}{4} \)
\( \frac{15}{4} \)
3\(\frac{3}{4}\)