Answer:
See below
Step-by-step explanation:
[tex]5^{-3}[/tex] - When you are raising a number to a negative power, it is the same as dividing 1 by that power when it is positive. So, [tex]5^{-3}[/tex] can be written as: [tex]\frac{1}{5^{3}}[/tex].
[tex]5^3[/tex] is 125, so we can substitute that in to get: [tex]\frac{1}{125}[/tex]
[tex]-5^{-3}[/tex] - This expression is the same as the one before, but it is negative. This means we can say [tex]-5^{-3} = -\frac{1}{125}[/tex]
[tex](-5^{-3})^{-1}[/tex] - We can start by writing [tex]-5^{-3}[/tex] as [tex]-1 * 5^{-3}[/tex]. Now, we can distribute the exponent -1, and simplify. Remember when raising a power in parenthesis to another power, you multiply them:
[tex](-1 * 5^{-3})^{-1}\\(-1)^{-1} * (5^{-3})^{-1}\\-1*5^3\\-1*125\\-125[/tex]
[tex](-5^{-3})^0[/tex] - We can start by writing [tex]-5^{-3}[/tex] as [tex]-1 * 5^{-3}[/tex]. Now, we can distribute the exponent 0, and simplify:
[tex](-1*5^{-3})^0\\(-1)^0 * (5^{-3})^0\\1 * 1\\1[/tex]
