Question

Simplify the expression.

(m^-1 m^5/m^-2)^-3

a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18

Answer 1

option d

Explanation:

`\sf \boxed{a^m*a^n = a^(m+n)\\\\}`

`\sf \left((m^(-1)m^(5))/(m^(-2)) \right)^(-3) =\left((m^(-1+5))/(m^(-2))\right)^(-3)`

`\sf = \left((m^4)/(m^(-2))\right)^(-3)\\\\`

`\boxed{(a^(m))/(a^(n))=a^(m+n)}`

`\sf = \left(m^(4-[-2])\right)^(-3)\\\\ =\left(m^(4+2)\right)^(-3)\\\\ = \left(m^6\right)^(-3)\\\\`

`\boxed{(a^(m))^n=a^(m*n)}`

`\sf= m^(6*(-3))\\\\ = m^(-18)`

`\boxed{a^(-m)=(1)/(a^m)}`

`\sf=(1)/(m^(18))`