Use index laws to evaluate simple fractional or negative powers
Index form is another way of writing numbers, which sometimes looks neater, or simpler. 49 can be written as 7^{2}, 9 can be written as 3^{2} and finally 200 can be written as 2^{3 }x 5^{2 }(8 x 25).
A number with a large index, such as 52^{4}, is a very big number. If we ever had to multiply something like 52^{4} x 520, it would take a long time, look messy, and involve having to write out number with dozens of digits.
Luckily, we have discovered special rules which can make the calculation much easier. Provided the base number is the same, we can just add the indices together
e.g. 51/3 x 51/3 = 51/3+1/3 = 52/3
This doesn’t work if the base numbers are different
e.g. 51/3 x 71/3 is NOT 52/3, or 352/3, or 122/3
In algebra, we can do the same thing, provided the letter is the same:
e.g. y2/7 x y3/7 = y2/7+3/7 = y5/7
e.g. s2 x s5 = s2+5 = s3
If we are dividing numbers in index form, we can subtract the indices.
e.g. y2/7 ÷ y3/7 = y2/73/7 = y1/7
e.g. s2 ÷ s5 = s25 = s7
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