Answer:
5^9
Step-by-step explanation:
125=5*5*5
125^3=125*125*125
125*125*125=3*(5*5*5)
the answer 5^9
The number as a power of 5 which is obtained by the number 125^3 using the power rule and simplifying is 5⁹.
The power rule states that, when the term is raised with a power which is again raised by another power, then this can be simply written as one power by multiplying both the power.
It has to write the number 125³ as a power of 5. Let the resultant number as a power of 5 is n. Thus,
[tex]n=125^3[/tex]
Rewrite the number with multiples of 125.
[tex]n=(5\times5\times5)^3\\n=(5^3)^3[/tex]
By the power rule, the above expression can be rewritten as,
[tex]n=(5)^{3\times3}\\n=(5)^{9}\\n=5^9[/tex]
Thus, the number as a power of 5 which is obtained by the number 125^3 using the power rule and simplifying is 5⁹.
Learn more about the power rule here;
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