Question

what is the simplified form of the expression [m^-1 m^5/m^-2]^3?

Answer 1

anything with a negative exponent in the numerator can be moved to the denominator. Likewise, a coefficient with a negative exponent in the denominator can be moved in to the numerator

m^-1 = 1/m
1/m^-2 = m^2
Therefore, you have (m^5*m^2)/m
= m^7/m
= m^6

now plug this in to the original problem
(m^6)^3 = m^18

Answer 2

Okay give me a moment. @mramosville

Answer 3

Actually I came up with the answer: 1/m^18 @mramosville

Answer 4

when you multiply same base and the powers
(m^-1)(m^5)(m^-2) =m^(-1+5-2) =m^2
when you raise a power to a power just multiply the powers
so (m^2)^3 = m^(2)(3) = m^6

Answer 5

correction
the original problem had divide by m^-2
same principle would apply
when you divide same base you subtract the powers

Answer 6

(m^6)^3 = m^18