write laws of indices and frame 3 examples for each laws of indices
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There are some fundamental rules or laws of indices which are necessary to understand before we start dealing with indices. These laws are used while performing algebraic operations on indices and while solving the algebraic expressions, including it.
Rule 1: If a constant or variable has index as ‘0’, then the result will be equal to one, regardless of any base value.
a0 = 1
Example: 50 = 1, 120 = 1, y0= 1
Rule 2: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable.
a-p = 1/ap
Example: 5-1 = ⅕, 8-3=1/83
Rule 3: To multiply two variables with the same base, we need to add its powers and raise them to that base.
ap.aq = ap+q
Example: 52.53 = 52+3 = 55
Rule 4: To divide two variables with the same base, we need to subtract the power of denominator from the power of numerator and raise it to that base.
ap/aq = ap-q
Example: 104/102 = 104-2 = 102
Rule 5: When a variable with some index is again raised with different index, then both the indices are multiplied together raised to the power of the same base.
(ap)q = apq
Example: (82)3 = 82.3 = 86
Rule 6: When two variables with different bases, but same indices are multiplied together, we have to multiply its base and raise the same index to multiplied variables.
ap.bp = (ab)p
Example: 32.52 = (3 x 5)2 = 152
Rule 7: When two variables with different bases, but same indices are divided, we are required to divide the bases and raise the same index to it.
ap/bp = (a/b)p
Rule 8: An index in the form of a fraction can be represented as the radical form.
ap/q = q√ap
Example: 61/2 = √6