Thread: negative indices

if 1/x^2 = x^-2/1 then why is 5/x^2 = 5x^-2 instead of x^-2/5?

Originally Posted by olivia59

if 1/x^2 = x^-2/1 then why is 5/x^2 = 5x^-2 instead of x^-2/5?

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"if 1/x^2 = x^-2/1 then why is 5/x^2 = 5x^-2 instead of x^-2/5? "

that blue thing "1/x^2 = x^-2/1" is wrong, this is correct: 1/x^2 = x^-2

this is correct, 5/x^2 = 5x^-2 not this 5/x^2= x^-2/5

rules of exponent:

(i) (x/y)^2 = x^2/y^2

(ii) 1/x^n = x^(-n) . . . . . . . . .

rule (ii) applies to your queries.