Exponents Examples
Example 1: Solve the following:
- 2.2.2.2
- 32.33
- (4.5)2
- (5)0
- 2-2
- 25/23
- [(3)1]2
- 43/2
- (4/3)2
Solution:
- 2.2.2.2 = 24 =16
- 32.33 = 3(2 + 3) = 35 = 243
- (4.5)2 = 42.52 = (16).(25) = 400
- (5)0 = 1
- 2-2 = 1/22 = 1/4
- 25/23 = 2(5-3) = 22 = 4
- [(3)1]2 = 3(1.2) = 32 = 9
- 43/2 = √(4)3 = √64 = 8
- (4/3)2 = 42/32 = 16/9
Example 2: Simplify:
- (23 ÷ 24)-2.23
- 3(-2)÷ 42
- 33.42/64
- (3-1 + 2-2 + 4-1)
Solution:
(1)
(23 ÷ 24)-2.23
= (23/24)-2.23
= [2(3 – 4)]-2.23
= [2-1]-2.23
= 2(-1).(-2).23
= 22.23
= 25 = 32
(2)
3(-2) ÷ 42
= 1/(3)2(4)2
= 1/9.16 = 1/144
(3)
33.42/64
= 33.42/(2.3)4
= 33.24/24.34
= 1/3
(4)
(3-1 + 2-2 + 4-1)
= (1/3 + 1/22 +1/4)
= (1/3 + 1/4 + 1/4)
= 5/6
Example 3: Find the value of x if (4)x + 12 = (4)2x + 6.(2)6
Solution:
(4)x+12 = (4)2x+6.(22)3
(4)x+12 = (4)2x+6.(4)3
(4)x+12 = (4)2x+6+3
(4)x+12 = (4)2x+9
Since, bases are equal powers gets equated
x +12 = 2x + 9
2x – x = 12 – 9
x = 3
Example 4: Find the value of {3434/3}1/4
Solution:
{3434/3}1/4 = {(73)4/3}1/4
= {7}3.(4/3).(1/4) = 7
Example 5: Find the value of x + y if:
(81)y = 27/(3)x, 4y= 256
Solution:
(34)y = (33)/(3)x
(3)4y = (3)3-x
Since, bases are equal then powers get equated
4y = 3-x ⇢ Equation (1)
4y = 256
4y = (4)4
y = 4
Putting the value of y in Equation 1,
4.4 = 3-x
16 = 3-x
x = -13
Now, we have to find value of x + y
x + y = -13+4 = -9
Example 6: If (-9)2x+7 = (-9)x. 81, then find the value of (x2 + 1)/(x2 – 12).
Solution:
(-9)2x+7 = (-9)x . 81
(-9)2x+7 = (-9)x . (-9)2
(-9)2x+7 = (-9)x+2
Since, bases are equal then powers get equated
2x + 7 = x + 2
2x – x = 2 – 7
x = -5
Now, we have to find value of (x2 + 1)/(x2 – 12)
(x2 + 1)/(x2 – 12) = [(-5)2 + 1]/[(-5)2 – 12]
= [25 + 1]/[25 – 12]
= 26/13
(x2 + 1)/(x2 – 12) = 2
Example 7: Find multiplicative inverse of [(-13)-1]2 ÷ (91)-1
Solution:
Let, x = [(-13)-1]2 ÷ (91)-1
x = (-13)-2 ÷ (91)-1
= (-1/132) ÷ (1/91)
= (-1/132) × 91
x = -7/13
Multiplicative inverse is given by 1/x i.e.
1/x = 1/(-7/13)
1/x = -13/7
Exponents
Exponents are the basic concept used in mathematics that are helpful in solving and understanding very large numbers. Suppose we have to simplify a very large number such as 10 multiplied by itself 10 times then the number is represented as, 1010 which is a very easy way of representing the numbers. Exponent is also called the power of a number. The exponent of the number can be integers or fractions, The fraction exponent is also called the radical.
Table of Content
- What are Exponents?
- Exponents Formulas
- Laws of Exponents
- Exponents with Fractions
- Exponent Table