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## How to Solve Indices with Casio fx991ms

INDICES
(1). Simplify 125^-1/3 × 49^-1/2 × 10^0
(A) 350 (B) 35 (C) 1/ 35 (D) 1 /350
Solution :-Using “CASIO
fx -991MS /570MS ”
When raising a negative fraction to the power put brackets to avoid errors when using the calculator i.e. 125(-1/3) except it is a positive whole number
[ON] [1] [2] [5] [^] [(] [(-)] [1] [a b /c] [3] [)] [X] [4] [9] [^] [(] [(-)] [1] [a b /c ] [2] [)] [X] [10] [^] [0] [=] ( 1/ 35 ) Option “C” is the correct answer
(2). Simplify 92^x-3 = 3^x+3
(A) -3 (B) 3 (C) 2 (D) 5
Solution using “CASIO fx -991MS ” calculator when performing calculations raised to the power i.e. 9 2x-3 or 3x+3 put brackets to avoid error i.e. 9 (2x-3) or 3 (x+3) since there is equal sign in the question given make left axis=9 2x-3 , right axis=3 x+3 Note:- left axis must be equal to right axis example a=a, or 31=31.
The left axis and the right axis must be the same. To trace the answer in the options given make x = any of the answers given in option A, B, C, D one after the other. If the left axis is equal to the right axis then the option is correct, but if the left axis is not equal to the right axis. then the options is wrong. Checking option A,B,C,D
Checking option (A)-3 make x=-3
Using CAS1O fx-991MS calculator
[ON] [(-)] [3] [SHIFT] [STO] [X] (x= -3)
Note:- Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [9] [^] [(] [2] [ALPHA] [X] [-] [3] [)] [=] (0.000000002) [3] [^] [(] [ALPHA] [X] [+] [3] [)] [=] (1)
Option (A) is wrong go to the next option
Checking option (B) 3 make x=3
[AC] [3] [SHIFT] [STO] [X] (x=3)
Press [↑] [↑] [=](729) Press [↑] [↑] [=](729)
If left axis is equal to Right axis, option (B) is correct
Checking option (C) 2 make x= 2
[AC] [2] [SHIFT] [STO] [X] (x=2)
Press [↑] [↑] [=] (9) Press [↑] [↑] [=] (243)
If left axis is not equal to right axis option (C) is wrong
Checking option (D) 5 make x=5
[ON] [5] [SHIFT] [STO] [X] (x=5)
Press [↑] [↑] [=] (4,782,969) Press [↑] [↑] [=] (6,561)
If left axis is not equal to right axis, option (D) is wrong
The correct answer is option (B)
(3). If 3^y+x = 9^y+x and 2^x–y = 8^x–3 find the values of x and y
(A)  4, 5 (B) 4, 3 (C) 3, -3 (D) 9, -9
x, y       x, y       x, y       x, y
Solution:- Using CASIO fx-991MS calculator
Put x and y in the given option above . Left axis must be equal to right axis, If the left axis is not equal to the right axis the option is wrong
3^y+x = 9^y+x…………………………….(1)
2^x–y = 8^x–3 …………………………….(2)
From equation….(1) left axis is = 3^y+x, right axis is = 9^y+x
Checking option(A) 4, 5 put x = 4 and y = 5
[ON] [4] [SHIFT] [STO] [X] (x = 4)
[AC] [5] [SHIFT] [STO] [Y] (y = 5)
Note:-Please use the key [AC] during calculcations after you press the key [ON] on any question given
[AC] [3] [^] [(] ALPHA] [Y] [+] [ALPHA] [X] [)] [=] (19,683) [9] [^] [(] [ALPHA] [Y] [+] [ALPHA] [X] [)] [=](387,420,489)
From equation 1 if the left axis is not equal to right axis option (A) is wrong. Since option (A) is wrong don’t bother to calculate equation 2 go to the next option
Checking option (B) 4, 3 make x = 4 and y = 3
[AC] [4] [SHIFT] [STO] [X] (x = 4)
[AC] [3] [SHIFT] [STO] [Y] (y = 3)
press [↑] [↑] [↑] [=] (2,187)
press [↑] [↑] [↑] [=] (4,782,969)
From equation 1 if the left axis is not equal to right axis option (A) is wrong. Since option (A) is wrong don’t bother to calculate equation 2, go to the next option
Checking option(C) 3, -3 make x = 3, and y = -3
[AC] [3] [SHIFT] [STO] [X] (x=3)
[AC] [(-)] [3] [SHIFT] [STO] [Y] (y=-3)
Press [↑] [↑] [↑] [=] (1)
Press [↑] [↑] [↑] [=] (1)
Since left axis is equation to right axis in equation 1. Equation 1 is correct to conclude go to the next equation by calculating equation 2 using CASIO
fx-991MS calculator
2^x–y = 8^x–3 ………………………………………(2)
Since x = 3 and y = -3
[AC] [2] [^] [(] [ALPHA] [X] [-] [ALPHA] [Y] [)] [=] (64) [8] [^] [ALPHA] [X] [-] [3] [)] [=] (1)
From equation 2 if the left axis is not equal to right axis option (C) is wrong. Since option(C) is wrong don’t go to the next option
Checking option (D) 9, -9   make x = 9 and y = -9
[AC] [9] [SHIFT] [STO] [X] (x = 9)
[AC] [(-)] [9] [SHIFT] [STO] [Y] (y = -9)
Press [↑] [↑] [↑] [↑] [↑] [=] (1) Press [↑] [↑] [↑] [↑] [↑] [=] (1) Press [↑] [↑] [↑] [↑] [↑] [=] (262,144) Press [↑] [↑] [↑] [↑] [↑] [=] (262,144)
The correct answer is option “D”

(NB: ^ is raise to power, × is multiplication sign)

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