Answer:
(a)
[tex]5^{-3}=\frac{1}{125}[/tex]
(b)
[tex]-5^{-3}=-\frac{1}{125}[/tex]
(c)
[tex](-5^{-3})^{-1}=-125[/tex]
(d)
[tex](-5^{-3})^{0}=1[/tex]
Step-by-step explanation:
(a)
[tex]5^{-3}[/tex]
we can use property of exponent
[tex]a^{-n}=\frac{1}{a^n}[/tex]
we get
[tex]5^{-3}=\frac{1}{5^3}[/tex]
[tex]5^{-3}=\frac{1}{5\times 5\times 5}[/tex]
[tex]5^{-3}=\frac{1}{125}[/tex]........Answer
(b)
[tex]-5^{-3}[/tex]
we can use property of exponent
[tex]a^{-n}=\frac{1}{a^n}[/tex]
we get
[tex]-5^{-3}=-\frac{1}{5^3}[/tex]
[tex]-5^{-3}=-\frac{1}{5\times 5\times 5}[/tex]
[tex]-5^{-3}=-\frac{1}{125}[/tex]........Answer
(c)
[tex](-5^{-3})^{-1}[/tex]
we can use property of exponent
[tex](a^{n})^m=a^{m\times n}[/tex]
we get
[tex](-5^{-3})^{-1}=(-5)^{-3\times -1}[/tex]
[tex](-5^{-3})^{-1}=(-5)^3[/tex]
[tex](-5^{-3})^{-1}=(-5)\times (-5)\times (-5)[/tex]
[tex](-5^{-3})^{-1}=-125[/tex]........Answer
(d)
[tex](-5^{-3})^{0}[/tex]
we can use property of exponent
[tex](a^{n})^m=a^{m\times n}[/tex]
we get
[tex](-5^{-3})^{0}=(-5)^{-3\times 0}[/tex]
[tex](-5^{-3})^{-1}=(-5)^0[/tex]
we can use property
[tex]a^0=1[/tex]
[tex](-5^{-3})^{0}=1[/tex]........Answer
