The equivalent expression of [tex](a^{-2}.8^{7} )^{2}[/tex] is [tex]a^{-4} .8^{14}[/tex].
What is an expression?
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given expression
[tex](a^{-2}.8^{7} )^{2}[/tex]
Using formula [tex]a^{-m} =\frac{1}{a^{m} }[/tex]
= [tex](\frac{8^{7} }{a^{2} } )^{2}[/tex]
= [tex]\frac{(8^{7}) ^{2} }{(a^{2}) ^{2}}[/tex]
Using [tex](a^{m} )^{n} =a^{m \times n}[/tex]
= [tex]\frac{8^{14} }{a^{4} }[/tex]
= [tex]a^{-4} .8^{14}[/tex]
Option C is correct.
The equivalent expression of [tex](a^{-2}.8^{7} )^{2}[/tex] is [tex]a^{-4} .8^{14}[/tex].
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