SOLUTION: simplify the expression (k^1/8)^(-15)/(k^7)^(1/2)

Question 706310: simplify the expression
(k^1/8)^(-15)/(k^7)^(1/2)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(k^(1/8))^(-15)/(k^7)^(1/2)
According to the the order of operations (aka PENDAS or GEMDAS) we should start with exponents. In both the numerator and denominator we have a power of a power. The rule for this is to multiply the exponents:
k^(-15/8)/k^(7/2)

What remains is a division. The rule for this is to subtract the exponents:
k^(-15/8)-(7/2)
As always, subtracting fractions requires the that the denominators be the same:
k^(-15/8)-(4/4)(7/2)
k^(-15/8)-(28/8)
Subtracting:
k^(-43/8)
This should be an acceptable answer. But sometimes answers with positive exponents are preferred. If so, then:
1/k^(43/8)
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