Answer:
1) [tex]\mathbf{5^{-3}=\frac{1}{125}}[/tex]
2) [tex]\mathbf{-5^{-3}=-\frac{1}{125}}[/tex]
3) [tex]\mathbf{(-5^{-3})^{-1}=-125}[/tex]
4) [tex]\mathbf{(-5^{-3})^0=1}[/tex]
Step-by-step explanation:
We need to solve the exponents
1) [tex]5^{-3}[/tex]
We know that: [tex]a^{-1}=\frac{1}{a}[/tex]
[tex]5^{-3}\\=\frac{1}{5^3}\\=\frac{1}{125}[/tex]
So, we get [tex]\mathbf{5^{-3}=\frac{1}{125}}[/tex]
2) [tex]-5^{-3}[/tex]
We know that: [tex]a^{-1}=\frac{1}{a}[/tex]
[tex]-5^{-3}\\=-\frac{1}{5^3}\\=-\frac{1}{125}[/tex]
So, we get [tex]\mathbf{-5^{-3}=-\frac{1}{125}}[/tex]
3) [tex](-5^{-3})^{-1}[/tex]
We know that: [tex](a^m)^n=a^{m*n}[/tex]
Using this rule:
[tex](-5^{-3})^{-1}\\=-5^{-3*-1}\\=-5^{3}\\=-125[/tex]
So, we get [tex]\mathbf{(-5^{-3})^{-1}=-125}[/tex]
4) [tex](-5^{-3})^0[/tex]
We know that: [tex](a^m)^n=a^{m*n}[/tex]
Using this rule:
[tex](-5^{-3})^0\\=-5^{-3*0}\\=-5^{0}\\We\:know\:a^0=1\\=1[/tex]
So, we get [tex]\mathbf{(-5^{-3})^0=1}[/tex]
