How do you express #t^-6# as a positive exponent?

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Answer 1 · 2018-01-19T17:01:55

#t^(-6)=1/t^6# See explanation.

If an expression has a negative exponent then to transform it to positive exponent you have to calculate the reciprocal of the expression:

#a^(-b)=1/a^b#

Now why is this true?
Well, let's use algebra.

Remember that #a^b*a^c=a^(b+c)#

Now, #a^b*a^(-b)=a^(b-b)=>a^0=1#
So we have #a^b*a^-b=1# We manipulate this to:
#a^(-b)=1/(a^b)#