Answer:
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]
Step-by-step explanation:
The given expression
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]
Writing a\times (-a)\times 13\times a\times (-a)\times 13 in power notation:
Let
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]
= [tex][13\times13][(a\times (-a)\times a\times (-a)][/tex]
As
[tex]13\times13 = 13^{2}[/tex] , [tex]a\times a = a^{2}[/tex] , [tex](-a)\times (-a) = (-a)^{2}[/tex]
So,
[tex]=[13^{2}][a^2\times (-a)^2][/tex]
As
[tex](-a)^2 = a^{2}[/tex]
So,
[tex]=[13^{2}][a^2\times a^2][/tex]
As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]
[tex]=[13^{2}][a^{2+2}][/tex]
As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]
[tex]=13^{2}\times a^{4}[/tex]
[tex]=a^{4}\times 13^{2}[/tex]
Therefore, [tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]
Keywords: power notation
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