Exponents is the power or degree to a given variable or number. The exponent can be any real number. There are many different properties of the exponents in algebra which help in solving many types of question having exponents. Mentioned below are some properties of exponents.
Multiplication rule: am * an = a(m+n) (Here the base is the same value a)
Division rule: am / an = a(m-n) (Here the base is the same value a)
Power of a power: (am)n = amn
Example 1: Find the value of x in the equation 3(x+2) = 27.
Solution: Here the given equation is 3(x+2) = 27.
We need to simplify the 27 further.
The number 27 can be written as 27 = 3* 3 * 3
So, 27 = 33
Now we get 3(x+2) = 33.
Since the base number is 3 we can equate the exponents.
X + 2 = 3 (subtracting 2 on both sides.)
X = 3 – 2.
Hence the value of x = 1.
Example 2: Find the x in the equation 102 = 1/100.
Solution: Here the given equation is 102 = 1/100.
The fraction, 1/100 = 100-1.
We need to simplify 100 here further.
The number 100 can be written as 100 = 10* 10
So, 100 = 102
Now we get 10(x) = (102)-1.
Using the power of power rule.
10(x) = (10-2)
Since the base number is 10 we can equate the exponents.
Hence the value of x = -2.