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Write [tex]$5 \cdot 5 \cdot 5 \cdot 5$[/tex] in exponential notation.

A. 625
B. [tex]$5^4$[/tex]
C. [tex]$4^5$[/tex]
D. [tex]$5^3$[/tex]

Answer :

We start with the expression

[tex]$$5 \cdot 5 \cdot 5 \cdot 5.$$[/tex]

Notice that the factor [tex]$5$[/tex] is multiplied by itself 4 times. When a number is multiplied by itself repeatedly, it can be written in exponential form. In general, if a number [tex]$a$[/tex] is multiplied by itself [tex]$n$[/tex] times, it is written as

[tex]$$a^n.$$[/tex]

Thus, since there are 4 factors of 5, we can write

[tex]$$5 \cdot 5 \cdot 5 \cdot 5 = 5^4.$$[/tex]

Additionally, evaluating [tex]$5^4$[/tex] gives

[tex]$$5^4 = 5 \times 5 \times 5 \times 5 = 625.$$[/tex]

So the expression in exponential notation is

[tex]$$\boxed{5^4}.$$[/tex]

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