Expert Quality Education - Problem Solving Series

Solution to the problem on exponents :

Learn the basics of Exponents and powers (classes 8 and 9 CBSE)

Exponents and powers are used for raising a number to the power of another as an equivalent of the number multiplied by itself as many times as the exponent. For example 2 "raised to the power" 2 is written as 2^2 which is 2 x 2.Review the law of exponents or indices which form the basics for handling powers in mathematics.

Basic Laws of exponents or indices

1. Product rule :   a^maⁿ = a^m+n  (Addition of powers of same base)

                            

2. Quotient rule :  a^m/aⁿ = a^{m – n} (difference in powers of same base)

3. Power of a power rule : (a^m)ⁿ = a^mn  (product of powers of same base)

4. Common power rule in product: a^mb^m = (ab)^m

5. Common power rule in quotient : a^m/b^m = ( a/b)^m             

6. Reciprocal rule (or negative exponent rule): a ^{– m}  = 1/a^m

            

                                                                    (or)   a ^m  = 1/a ^{– m}

 Here is another problem:

If 9 ^{x – 1}  = 3^{2 x – 1} – 162 , find the value of x.

We will try to solve the problem in the same manner as we solved the previous one.