Respuesta :

luisejr77

Answer: [tex]n=0[/tex]

Step-by-step explanation:

You need to remember that:

[tex]a^n=a^m\\n=m[/tex]

By the Power of a power property:

[tex](a^m)^n=a^{mn}[/tex]

By the Negative exponent rule:

[tex]a^{-1}=\frac{1}{a}[/tex]

Therefore, having the expression [tex](\frac{1}{9} )^{2n}=27^{n}[/tex]:

Descompose 27 and 9 into their prime factors:

[tex]27=3*3*3=3^3[/tex]

[tex]9=3*3=3^2[/tex]

Rewrite the expression and simplify. Then:

[tex](3^{-2})^{2n}=(3^3)^n\\3^{-4n}=3^{3n}\\-4n=3n\\-4n-3n=0\\n=0[/tex]

ShyzaSling

Answer:

n=0

Step-by-step explanation:

Given in the question an equation

[tex]\frac{1}{9}^{2n}=27^{n}[/tex]

we can write

[tex]\frac{1}{9}[/tex]

as

[tex](\frac{1}{3})^{2}[/tex]

further as

[tex]3^{-2}[/tex]

so

[tex]3^{-2(2n)}=3^{3n}[/tex]

[tex]3^{-4n}=3^{3n}[/tex]

Since now the base is same

and we know that

[tex]x^{n}=x^{m}\\n=m[/tex]

-4n = 3n

n cancel out which means n =0

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