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Created: 22 Aug, 2010; Last Modified: 29 Apr, 2018 Algebra II - 02Indices (Exponents)If n is a positive integer, then by definition, Case: zero exponentWhen the value of the power is zero (n .......(1)
This implies that any quantity with a zero exponent has a value of Thus,
Case: negative exponentWhen the value of the exponent is negative ( .......(2)
Thus, if n is a positive integer,
In other words, a number raised to a negative exponent is the reciprocal of that number raised to a positive exponent. The corollary of Eq. is: .......(3)
This further implies that any factor with an exponent can be relocated from the numerator to the denominator, or vice-versa, by changing the sign of the exponent. Thus,
Case: fractional exponentWhen the value of the exponent is fractional (of form
.......(4)
The above means that a raised to the power of
In other words, when a number is raised to a fractional power, the exponent of the number is the numerator of the fraction and the root of the number is the denominator of the fraction. As a corollary of Eq. .......(5)
Thus, (Note: the symbol Laws of IndicesThe following laws hold for all integral (positive and negative) and fractional values of m and n, as long there is no scope for division by Product LawWhen two numbers having the same base are multiplied, the indices are added. .......(6) Evaluate (i)
(i)
(ii)
Quotient LawWhen a number is divided by another having the same base, the indices are subtracted. .......(7) Evaluate (i)
(i)
(ii)
Power LawWhen a number raised to a power is further raised to a power, the indices are multiplied. .......(8) Evaluate (i)
(i)
(ii)
Given
Expressing This implies that (i) Equating the exponents of the same bases, we find that p (ii)
Find the value of x, if
From the above, once the base (i.e.
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Otherwise, send an email to feedback@mentorials.com with subject line: "Feedback: Indices (Exponents)". List of ReferencesBansal, RK, Concise Mathematics I.C.S.E., Part I – Class IX, New Delhi: Selina Publishers, 2005. BibliographyBird, J, Basic Engineering Mathematics, 4th edn, Oxford, UK: Elsevier, 2005. Gupta, SD & Banerjee, A, ICSE Mathematics for Class 9, Patna, India: Bharati Bhawan, 2003. Hall, HS & Knight, SR, Elementary Algebra for Schools, metric edn, Agra, India: AK Publications, 1966.
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