elenamcdonald21
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Which expressions are equivalent to the one below? Check all that apply.

25^x/
5^x
a. 5^x*5^x/5^x
b. (25-5)^x
c. 25^x
d. 5^x
e. 5
f. (25/5)^x

need answer ASAP!!!!!!!!!!!!!!!!!

Respuesta :

frika

Use two main properties for powers:

1. [tex](a^m)^n=a^{m\cdot n};[/tex]

2. [tex]\dfrac{a^m}{a^n}=a^{m-n}.[/tex]

The expression [tex]\dfrac{25^x}{5^x}[/tex] can be simplified in following way:

[tex]\dfrac{25^x}{5^x}=\dfrac{(5^2)^x}{5^x}=\dfrac{5^{2x}}{5^x}=5^{2x-x}=5^x.[/tex]

Then the expression [tex]\dfrac{25^x}{5^x}[/tex] is equivalent to [tex]5^x.[/tex]

Answer: correct choice is D

OlanmaE

The expressions that are equivalent to the one below are:

  • d. 5^x
  • f. (25/5)^x

What is the rule for the product of factors?

According to the rule guiding the product of factors, each factor is raised to  the power expressed there. So, for the equation above,

[tex]25^x/ 5^x\\\\= (25/5)^x\\\\= 5^x\\\\[/tex]

So, options D and F are equivalents of the equation.

Learn more about the product of factors here:

https://brainly.com/question/596505

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