2k^-1/18m^-3
2k^-1/18m^-3 = 18m^3/2k
To simplify the given expression 2k^-1/18m^-3, we can apply the rule of negative exponents.
Any number raised to the power of -1 is equivalent to its reciprocal. So, k^-1 is equal to 1/k. Similarly, m^-3 is equal to 1/m^3.
Substituting these values, the expression becomes:
2(1/k)/(18(1/m^3))
Simplifying further, we can multiply the numerator and denominator of the fraction by k and m^3, respectively:
(2/k)/(18/m^3)
Now, to divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, we can rewrite the expression as:
(2/k) * (m^3/18)
Multiplying the numerators and the denominators, we get:
2m^3/(18k)
Finally, we can simplify the expression by canceling out the common factors in the numerator and denominator. In this case, both 2 and 18 can be divided by 2:
m^3/9k