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In the previous grade, we have learnt about exponent. Let us recall them.
 
We can write the number \(729\) as \(9 \times 9 \times 9 = 9^3\). Here, the number \(9\) is the base and \(3\) is the exponent. The exponent is also called as index.
 
Here, we have found the value of \(9^3\). Similarly, we can find the value of \(9^{-3}\) which is the multiplicative inverse of \(9^3\). That is, \(9^3 \times 9^{-3} = 9^{3 - 3} = 9^0 = 1\).
 
Hence, we can write \(9^{-3}\) as \(9^{-3} = \frac{1}{9^{3}}\)
In general, we can say that \(x^{-n} = \frac{1}{x^n}\)
Consider the numbers with some powers like am,bn,...
 
Here \(a\) and \(b\) the base and \(m\) and \(n\) are its respective exponents.
 
The law of exponents are as follows:
 
(i)aman=am+n(ii)amn=amn(iii)aman=(a)mn,wherem>n.(iv)ambm=(ab)m
Example:
1. Consider 3536,
 
Here the base(3) is the same but the exponents \(5\) and \(-6\) are different.
 
Comparing the property aman=am+n with the expression,
 
3536=356=31=13.
 
 
2. Let us take another expression 935.
 
Here the base (9) is the same, but the exponents \(3\) and \(5\) are different.
 
Comparing the property amn=amn with the expression,
 
935=93×5=915.
 
3. Let the next expression be 2743.
 
Here the base values are \(2\) and \(4 = 2^2\), and the exponents are \(7\) and \(3\).
 
2743=27223
 
Applying the property amn=amn,
 
27223=2726
 
Now applying aman=(a)mn,wherem>n.
 
2726=276=21=2