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Sagot :
Sure, let’s solve each part step-by-step.
(i) [tex]$\left(\frac{1}{2}\right)^{-1}$[/tex]
To find the inverse of a number [tex]\( n \)[/tex], you raise [tex]\( n \)[/tex] to the power of -1.
[tex]\[ \left(\frac{1}{2}\right)^{-1} = 2 \][/tex]
So, [tex]\(\left(\frac{1}{2}\right)^{-1} = 2.0\)[/tex].
(ii) [tex]\(3^{-1}\)[/tex]
For this part, you also raise the number 3 to the power of -1.
[tex]\[ 3^{-1} = \frac{1}{3} = 0.3333333333333333 \][/tex]
So, [tex]\(3^{-1} = 0.3333333333333333\)[/tex].
(iii) [tex]\((-6)^{-1}\)[/tex]
When finding the inverse of -6, you raise it to the power of -1.
[tex]\[ (-6)^{-1} = \frac{1}{-6} = -0.16666666666666666 \][/tex]
So, [tex]\((-6)^{-1} = -0.16666666666666666\)[/tex].
(iv) [tex]\(\left(\frac{1}{-2}\right)^{-1}\)[/tex]
Lastly, we find the inverse of [tex]\(\frac{1}{-2}\)[/tex].
[tex]\[ \left(\frac{1}{-2}\right)^{-1} = -2 \][/tex]
So, [tex]\(\left(\frac{1}{-2}\right)^{-1} = -2.0\)[/tex].
Therefore, the answers are:
[tex]\[ (i) \left(\frac{1}{2}\right)^{-1} = 2.0 \][/tex]
[tex]\[ (ii) 3^{-1} = 0.3333333333333333 \][/tex]
[tex]\[ (iii) (-6)^{-1} = -0.16666666666666666 \][/tex]
[tex]\[ (iv) \left(\frac{1}{-2}\right)^{-1} = -2.0 \][/tex]
(i) [tex]$\left(\frac{1}{2}\right)^{-1}$[/tex]
To find the inverse of a number [tex]\( n \)[/tex], you raise [tex]\( n \)[/tex] to the power of -1.
[tex]\[ \left(\frac{1}{2}\right)^{-1} = 2 \][/tex]
So, [tex]\(\left(\frac{1}{2}\right)^{-1} = 2.0\)[/tex].
(ii) [tex]\(3^{-1}\)[/tex]
For this part, you also raise the number 3 to the power of -1.
[tex]\[ 3^{-1} = \frac{1}{3} = 0.3333333333333333 \][/tex]
So, [tex]\(3^{-1} = 0.3333333333333333\)[/tex].
(iii) [tex]\((-6)^{-1}\)[/tex]
When finding the inverse of -6, you raise it to the power of -1.
[tex]\[ (-6)^{-1} = \frac{1}{-6} = -0.16666666666666666 \][/tex]
So, [tex]\((-6)^{-1} = -0.16666666666666666\)[/tex].
(iv) [tex]\(\left(\frac{1}{-2}\right)^{-1}\)[/tex]
Lastly, we find the inverse of [tex]\(\frac{1}{-2}\)[/tex].
[tex]\[ \left(\frac{1}{-2}\right)^{-1} = -2 \][/tex]
So, [tex]\(\left(\frac{1}{-2}\right)^{-1} = -2.0\)[/tex].
Therefore, the answers are:
[tex]\[ (i) \left(\frac{1}{2}\right)^{-1} = 2.0 \][/tex]
[tex]\[ (ii) 3^{-1} = 0.3333333333333333 \][/tex]
[tex]\[ (iii) (-6)^{-1} = -0.16666666666666666 \][/tex]
[tex]\[ (iv) \left(\frac{1}{-2}\right)^{-1} = -2.0 \][/tex]
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