Simplify each exponential expression?
52) 35a^14b^6/-7a^7b^3 = -5a^7b^3 54) 20b^10/10b^20 = 2/b^10 56) (10x^2)^-3 = (1E-3)(x^-6) 58) 10x^4y^9/30x^12y^-3 = y^12/3x^3 60) (3x^4/y)^-3 = y^3/27x^12 62) (-30a^14b^8/10a^17b^-2)^3 = (-3b^10/a^3)^3 = -27b^30/a^9 64) 1 - .--
Simplify the following rational expressions!?!?
As with numerical fractions when adding or subtracting, convert both denominators to a common denominator and adjust the numerators accordingly. 1) 2/a + 5/b...........common denominator is ab = (2b/ab) + (5a/ab) = (5a + 2b) / ab 2) 4/x - 3/2y.........common denominator is 2xy = 4*2y/2xy - 3*x/2xy = (8y - 3x) / 2xy 3) (b² - 4b) / (b² - b - 12) The numerator can be factored, b² - 4b = b(b - 4) The denominator can be factored, b² - b - 12 = (b - 4)(b + 3) Replacing these factored expressions gives :- b(b - 4) /(b - 4)(b + 3) = b / (b + 3) 4) (7a/14b) x (6b²/a) = (7a * 6b²) / (14b * a) = 42ab² / 14ab = 3b
Simplify (7b-1)/(b^2+b-2 -6)/(b-1)?
(7b-1)/(b^2+b-2 -6)/(b-1) =(7b-1) / (b-1)(b^2+b-8)
Can anyone tell the solution of this question [math](7 + 5 \sqrt{2})^{1/3} + (7- 5\sqrt{2})^ {1/3}=?[/math]
Take 7+5(2)^(1/2)=a^3 and 7-5(2)^(1/2)=b^3. a^3 b^3=49-50=-1=>a b=-1 and a^3+b^3=14.We want the value of a+b. Denote a+b =x.x^3=a^3+b^3+3 a b(a+b)=14-3x=>x^3+3 x-14=0=>(x-2)(x^2+2 x+7)=0=>x=2 (as x^2+2 x+7 >0) Hence (7+5(2)^(1/2))^(1/3)+(7-5(2)^(1/2))^(1/3)=2
Math problems! 10 points?
my teacher gave us these math problems but i have no textbook and i am very confused! if anyone could help me at all i would really appreciate it! thank you a^2 -9ab+14b^2 ------------------------- a^2b-7ab^2 45a^5b(8-a) ------------------ 20a^2b^3(a-8) 6ab^2-24a --------------- 18a^2-9a^2b 49a^2+14ab+b^2 ------------------------- 7ab^4=b^5 20a^2b+10ab ------------------- 16a^2b^3+16ab^3
Plz factorize (2a+4b)^2 -(2a+4b)(6a-14b)?
hi guyz plz factorize this question. and explain it in steps. i have a test tommorow and this is the only type of question i dont understand. i will appreciate the help. plz factorize in steps so it will be easy for me to understand.
I need to solve for the three unknowns a, b, and c in the following equations. 3a - 5c = -9, 2a + 7b = 11, a + b + c = 6. The answer is (2, 1, 3), but how do I get there?
First of all, check the equations. It has 3 variables (A, B, C) and 3 independent equations. So it's solvable. (If it's not solvable, then we cannot have a exact answer.)Before doing any calculate, exam each equation. In the first one, it tells the relationship between A and C. The second one, A and B. The third one, A , B, C. It give us a hint. We can use A to express B or C. B=(11-2A)/7C=(3A+9)/5Then put them into the third equation.A+ (11-2A)/7 +(3A+9)/5 =6Only ONE variable, A, in this equation. We can get A form this one.Multiply 35 to both side of the equation. (35 is the least common multiple for 7 and 5)We got, 35A + 55 - 10A +11A +63 = 210Then we get A=2.And, B=(11-2A)/7 = 1C=(3A+9)/5 = 3
If [math]a+b=7 [/math]and [math]ab=12[/math], then what is the value of [math]a^2-ab+b^2[/math]?
The answer is 13.Method 1:Plot graph of [math]a + b = 7 [/math]which is a straight line intersecting a and b axis (rectangular coordinate system) at (7,0) and (0,7) respectively.Again plot graph of [math]ab=12 [/math]which is a rectangular hyperbola.The vertical and horizontal axis are the a and b axis. The graph line in red is of [math]a + b = 7[/math] and the one in blue is of [math]ab = 12. [/math]The intersection point of both the graph lines gives us the value of a and b. As we can see in the graph the values are (3, 4) and (4, 3).Case 1: when a = 3 and b = 4[math]a^2 - ab - b^2 = (3^2) - (3*4) - (4^2) = 13[/math]Case 2: when a = 4 and b = 3[math]a^2 - ab - b^2 = (4^2) - (4*3) - (3^2) = 13[/math]Hence either ways the answer is 13.Method 2:It may be done simpky as followsGiven, [math]a + b = 7[/math][math](a + b)^2 = 7^2 [/math][math]a^2 + 2ab + b^2 = 49[/math]Subtracting [math]3ab[/math] from both sides[math]a^2 - ab - b^2 = 49 - 3ab[/math]We are given the value of ab = 12 in question hence,[math]a^2 - ab - b^2 = 48 - 3(12) = 49 - 36 = 13[/math]Hence the answer is 13.