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Exponents and power

 Eg: 4^2=4*4 ; in this equation 2 is called power of 4,4 is called base
           Power of a number means:multiply of a particular number with itself
           till the power of a number.more eg are given below: 13^3=13*13*13 , 23^3=23*23*23;
           Square of a number : it means multiply with the no. itself Eg: 45^2 = 45*45
           cube of a number:it means multiply the no. with itself 3 times Eg:80^3=80*80*80
           square root: Eg:36 =6*6 square root of 36=6 , 64=8*8 square root of 64=8
           cube root :  Eg: 512=8*8*8, 216=6*6*6 ,so cube root of 512=8 .
           (x)-b/a = (1/x)b/a  ,(x/y)-b/a= y/xb/a
 
           1.Find the square of 15
           Ans:15*15=225
           2.Find the cube of 15
           Ans:15*15*15=3375
           3.Find (2/3) 5
            Ans:(2/3)*(2/3)*(2/3)*(2/3)*(2/3)=64/234  
            
 Prime factorization method to find the square root and cube root of any no:
    a)1024  2| 1024
            2|512
            2|256
            2|128
            2|64
            2|32
            2|16
            2|8
            2|4
            2|2
              1
2*2,2*2,2*2,2*2,2*2.so square root be 2*2*2*2*2=16 
b)250000 2|250000
         2|125000
         2|62500
         2|31250
         5|15625
         5|3125
         5|625
         5|125
         5|25
         5|5
           1


2*2,2*2,5*5,5*5,5*5.so square root would be 2*2*5*5*5 =500 
 prime factorization method to find the cube root of any no:
a) 4096 2|4096
        2|2048
        2|1024
        2|512
        2|256
        2|128
        2|64
        2|32
        2|16
        2|8
        2|4
        2|2
          1
 2*2*2,2*2*2,2*2*2,2*2*2 so the cube root would be 2*2*2*2=16  
        b) 125,000,000
         5|125000000
         5|25000,000
         5|5,000,000
         5|1,000,000
         5|200,000
         5|40,000
         2|8,000
         2|4,000
         2|2,000
         2|1,000
         2|500 
         2|250
         5|125
         5|25
         5|1
5*5*5,5*5*5,5*5*5,2*2*2,2*2*2 ,so cube root would be 500. 

EASY LEVEL



1.Find the square of following:

a)36
Ans : a)square= 36*36=576
check the answer!!!


b) 45

c)13

d)29

2.Find the cube of following:

a)56

b)67

c)56

d)80

e)100


Ans : cube of 100 = 100*100*100=1000,000
check the answer!!!
3.Find the difference between cube of 13 and 14

4.Find the addition of square of 16 and square of 17.

5.Find the addition of square of 30 and cube of 30.



6.Find the value of following

a) (35/15) 3-5-2

Ans : a) 35 = 3*3*3*3*3=729
check the answer!!!
b) (5/3)-2

c)(1/3)-5*(1/3)3

d)(23/7)0*(6)0/80

e)15-3/3-3

7.Simplify:

a)342/(23*172)

b)(332/3 +222) /33*113

c)(1254/5 +1211/2128-2/5

d)(497/2*-2/3)-2/3/ 167/4

e){(1048)3/2/2411-3/4}+(2/3)3

8) Convert the following into power notation

a) 625/2401 b) -144/243 c)
9) compare 6power2 and 2power6

MEDIUM LEVEL



1.Find The square root of following using prime factorization method.

a)144

Ans : a) 2|144
2|72
2|36
2|18
3|9
3 2*2*2*2*3*3=(2*2*3)(2*2*3) so,square root= 2*2*3=12
check the answer!!!
b)6724

2)Write in ascending order :
Ans : a)Perimeter=4*(side)
=5*4=20cm
check the answer!!!
2.Check whether 2345 is a perfect square or not.

3.Check whether 23456 is a perfect square or not.

4.Area of a square plot is 8100m.sq.Find the side of that square plot.

5.Find the hypotenuse of a right angled traingle when it's base n height is 5cm ,4cm.

6.Find the square root of 64 and 144 and add it.

7.How many no. should be multiplied to 2592 to get perfect square.

Ans : a)2592
2|2592
2|1296
2|648
2|324
2|162
3|81
3|27
3|9
3|3
2*2*2*2*2*3*3*3*3 = (2*2)*(2*2)*(3*3)*(3*3)*(2)
only 2 is not in pair,so 2 is multiplied by 2592 to get perfect square
check the answer!!!
8.How many no. should be divided by 15552 to get perfect square.

9.How many no.should be divided by 1728 to get perfect square.

Ans:a)1728
2|1728
2|864
2|432
2|216
2|108
2|54
3|27
3|9
3|3
1
(2*2)*(2*2)*(2*2)*(3*3)*(3)
3 is not in pair,1728 should be divided by 3 to get perfect square
check the answer!!!

HIGH LEVEL



1.Find the cube root of following:

a) 46656

Ans: 3|46656
3|15552
3|5184
2|1728
2|864
2|432
2|216
2|108
2|54
3|27
3|9
3|3
1
(2*2*2)*(2*2*2)*(3*3*3)*(3*3*3)
so,the cube root would be 2*3*2*3=36
check the answer!!!
b) 2744.

c) 24696.

d)3375.

2.Check whether the following no. is perfect cube or not.

a)569 b) 1028 c)10125 d)12167 e) 2401

3.How many no. should be multiplied to 169 to get perfect cube.

4.How many no. should be multiplied to 507 to get perfect cube.

5.How many no. should be divided to 546750 to get perfect cube.

6.How many no.should be divided to 20736 to get perfect cube.

7.Find the side of a cube when it's volume is 4096sq.unit.

volume = side 3
so, side = (volume)1/3
side = (4096) 1/3
2|4096
2|2048
2|1024
2|512
2|256
2|128
2|64
2|32
2|16
2|8
2|4
2|2
1
= (2*2*2)*(2*2*2)*(2*2*2)*(2*2*2)
16,so side = 16 unit
check the answer!!!
8) Evaluate: a) (239/27)0*(63)0/8110

b) (123/7)-1*(6)1*8991

c) 1-37+(1)40/10

d)(34)1-(16)1/4*360

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