Respuesta :

Hagrid
In multiplying quantities of the same base, the product is simply the base raised to a power that is the sum of the individual powers of the factors. That is, [tex](a^n)(a^m)= a^{n+m}[/tex]

The term [tex]5^{11}[/tex] can be expressed as the product of two factors with the same base (which is five) and whose powers add up to 11. Three examples are:
[tex](5^1)(5^{10}) = 5^{1+10} = 5^{11} \\ (5^5)(5^6) = 5^{5+6} = 5^{11} \\ (5^8)(5^3) = 5^{8+3} = 5^{11}[/tex]
facundo3141592

By using properties of powers, we can find:

[tex]5^{11} = 5^9*5^2\\\\5^{11} = 5^8*5^3\\\\5^{11} = 5^7*5^4[/tex]

How to find equivalent expressions?

Here we need to remember the powers property:

[tex]a^n*a^b = a^{n + b}[/tex]

So we can rewrite:

[tex]5^{11} = 5^n*5^m[/tex]

Always that n + m = 11.

With that in mind, 3 possible forms of writing that expression is:

[tex]5^{11} = 5^9*5^2\\\\\\5^{11} = 5^8*5^3\\\\5^{11} = 5^7*5^4[/tex]

In all of these cases, the sum of the two exponents in the right side is 11.

If you want to learn more about powers:

https://brainly.com/question/11975096

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