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Simplify.

Rewrite the expression in the form [tex][tex]$4^n$[/tex][/tex].

[tex]\left(4^2\right)^4 = [/tex] [tex]\square[/tex]


Sagot :

Let's start by simplifying the given expression step-by-step.

Given the expression:
[tex]\[ \left(4^2\right)^4 \][/tex]

We can simplify this using the power of a power rule, which states:
[tex]\[ (a^m)^n = a^{m \cdot n} \][/tex]

In this case, our base [tex]\(a\)[/tex] is [tex]\(4\)[/tex], our inner exponent [tex]\(m\)[/tex] is [tex]\(2\)[/tex], and our outer exponent [tex]\(n\)[/tex] is [tex]\(4\)[/tex]. Applying the power of a power rule:

[tex]\[ \left(4^2\right)^4 = 4^{2 \cdot 4} \][/tex]

Now, we just need to perform the multiplication in the exponent:

[tex]\[ 2 \cdot 4 = 8 \][/tex]

Therefore, we can rewrite the expression as:

[tex]\[ 4^8 \][/tex]

So, the simplified form of the given expression [tex]\(\left(4^2\right)^4\)[/tex] is [tex]\(\boxed{4^8}\)[/tex].