INTRODUCTION AND RULES OF EXPONENTS
We are already aware of that- the number multiplied by itself repeatedly is called the power of the number. The number is called the “BASE” and the number of times it is multiplied is called the “INDEX” or “EXPONENTS”, the index is written or mentioned on the upper right-hand side of the symbol for a literal or a constant.
Example –
1) In, a⁶ = a X a X a X a X a X a, we should read as ‘a’ to the power 6 (Six), base = a, index = 6.
2) In, b⁸ = b X b X b X b X b X b X b X b, we should read as ‘b’ to the power 8 (Eight), base = b, index = 8.
3) In, yᶟ = y X y X y, we should read as ‘y’ to the power 3 (Three) or ‘y’ cubed (or cube), base = y, index = 3.
4) In, z² = z X z, we should read as ‘z’ to the power of 2 (Two) or ‘z’ square ( or squared), base = z, index = 2.
5) z¹ = z
6) (-1)ⁿ = 1, when index ‘n’ is even
7) (-1)ⁿ = - 1, when index ‘n’ is odd
1
8) Z X --------- = 1
Z
1
9) Z ÷ Z = Z X ---------- = 1
Z
1
10) ----------- = a⁻ᵐ
aᵐ
This is called the Reciprocal of a power is written as a power with an index equal to the negative of the index of the power.
11) As we all know that, the laws of Multiplication – aᵐ X aⁿ = aᵐ⁺ⁿ, where ‘m’ & ‘n’ are numbers, and ‘a’ is a non-zero number.
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12) The laws of division, aᵐ ÷ aⁿ = aᵐ X --------- = aᵐ⁻ⁿ,
aⁿ
where ‘m’ & ‘n’ are numbers, and ‘a’ is a non-zero number.
13) The laws of power, (aᵐ)ⁿ = aᵐⁿ, where ‘m’ & ‘n’ are numbers, and ‘a’ is a non-zero number.
14) where ‘a’ is non zero number but the index is ‘0’ (zero), then a⁰ = 1
15) laws of the power of a product, ( a X b )ⁿ = aⁿ X bⁿ
aⁿ
and, (a / b)ⁿ = ---------- = aⁿ / bⁿ
bⁿ