Question

Упростите выражения : а) (1+ а/b) : (1-a/b) = b) 5- 5a+2b/ 2a * (1/5a+2b + 1/5a-2b) = c) 4 1/6 a^8 b^5 * (-1 1/5 a^5 b) ^3 =

Answer 1

Когда умножаем степени, показатели степеней надо складывать

Answer 2

a) (1+ а/b) : (1-a/b) =

We can simplify this expression by multiplying both the numerator and denominator by b to get rid of the fractions:

(1+ а/b) : (1-a/b) = [(b + a)/b] : [(b - a)/b]

Next, we can simplify the expression by multiplying both the numerator and denominator by the common denominator (b - a):

[(b + a)/b] : [(b - a)/b] = (b + a) : (b - a)

Therefore, the simplified expression is (b + a) : (b - a).

b) 5- 5a+2b/ 2a * (1/5a+2b + 1/5a-2b) =

We can start by simplifying the expression in parentheses by finding a common denominator:

1/5a+2b + 1/5a-2b = (5a-2b+5a+2b)/(25a^2-4b^2) = 10a/(25a^2-4b^2)

Substituting this back into the original expression gives:

5-5a+2b/2a * 10a/(25a^2-4b^2)

We can simplify this by canceling out common factors:

5-5a+2b/2a * 10a/(25a^2-4b^2) = (5-5a+2b)/(5a^2-b^2)

Therefore, the simplified expression is (5-5a+2b)/(5a^2-b^2).

c) 4 1/6 a^8 b^5 * (-1 1/5 a^5 b) ^3 =

We can start by converting the mixed number to an improper fraction:

4 1/6 = (4*6 + 1)/6 = 25/6

Next, we can simplify the expression inside the parentheses by adding the mixed number to -1 to get a fraction:

-1 1/5 = (-1*5 + 1)/5 = -4/5

Substituting these back into the original expression gives:

25/6 a^8 b^5 * (-4/5 a^5 b)^3

We can simplify this by first raising the fraction to the third power:

(-4/5)^3 = -64/125

Then we can simplify the expression by multiplying the coefficients and adding the exponents of the variables:

25/6 * (-64/125) * a^(8+5*3) * b^(5+3) = -16/15 a^23 b^8

Therefore, the simplified expression is -16/15 a^23 b^8.