IMPORTANT RULES OF EXPONENTS
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
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8) Z X -------- = 1
Z
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9) Z ÷ Z = Z X --------- = 1
Z
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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) 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 index is ‘0’ (zero), then a⁰ = 1
15) laws of th power of a product, ( a X b )ⁿ = aⁿ X bⁿ
aⁿ
and, (a / b)ⁿ = ---------- = aⁿ / bⁿ
bⁿ