Answer :
Using rule of exponents, [tex]a^{12}\times a^4=a^8\times a^8[/tex] i.e., a to the 12th power times a to the fourth power equal a to the eighth power times a to the eighth power.
For given question,
first we write each statement as a mathematical expression.
a to the 12th power = [tex]a^{12}[/tex]
a to the fourth power = [tex]a^4[/tex]
a to the eighth power = [tex]a^8[/tex]
a to the eighth power = [tex]a^8[/tex]
We need to check, whether a to the 12th power times a to the fourth power is equal to a to the eighth power times a to the eighth power.
i.e., to check [tex]a^{12}\times a^4=a^8\times a^8[/tex]
Consider, ⇒ LHS = [tex]a^{12}\times a^4[/tex]
⇒ LHS = [tex]a^{12+4}[/tex] .....................(product rule of exponents)
⇒ LHS = [tex]a^{16}[/tex] ..................(1)
Now consider, ⇒ RHS = [tex]a^8\times a^8[/tex]
⇒ RHS = [tex]a^{8+8}[/tex] .....................(product rule of exponents)
⇒ RHS = [tex]a^{16}[/tex] ...................(2)
From (1) and (2),
LHS = RHS
Therefore, [tex]a^{12}\times a^4=a^8\times a^8[/tex] i.e., a to the 12th power times a to the fourth power equal a to the eighth power times a to the eighth power.
Learn more about the powers here:
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