Answer:
[tex]4^{-2}[/tex]
Step-by-step explanation:
Given the expression: [tex](4^{6})(4^{-8})[/tex]
The two terms have the same base 4. Therefore, we can apply the addition law of indices to simplify.
Addition Law of Indices: [tex]a^x \cdot a^y=a^{x+y}[/tex]
Therefore:
[tex](4^{6})(4^{-8})\\=4^{6+(-8)}\\=4^{6-8}\\=4^{-2}[/tex]
Therefore:
[tex](4^{6})(4^{-8})=4^{-2}[/tex] in the form [tex]4^n[/tex]
The equivalent expression of [tex](4^{6})(4^{-8})[/tex] is [tex]4^{- 2}[/tex]
The expression is given as:
[tex](4^{6})(4^{-8})[/tex]
Rewrite the expression as follows:
[tex]4^{6} * 4^{-8}[/tex]
Apply the product law of indices
[tex]4^{6 - 8}[/tex]
Evaluate the difference
[tex]4^{- 2}[/tex]
Hence, the equivalent expression of [tex](4^{6})(4^{-8})[/tex] is [tex]4^{- 2}[/tex]
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