m=3^n is given expressions 81^(2n+9) in terms of m

[mathz]

Hello people,

we (my kid and I) have this task for homework.

m=3^n is given expressions 81^(2n+9) in terms of m

Please, can you help me for solve?

Thank you

 

[pka]

m=3^n is given expressions 81^(2n+9) in terms of m
Please, can you help me for solve?

Here is a start. \(\displaystyle 81^{2n+9}=\left(3^4\right)^{2n+9}=3^{8n+36}\).
Also \(\displaystyle m^2=3^{2n}\)

 

[mmm4444bot]

:idea: Do you (or your kid) have a list of exponent properties at hand? :cool:

 

[mathz]

Here is a start. \(\displaystyle 81^{2n+9}=\left(3^4\right)^{2n+9}=3^{8n+36}\).
Also \(\displaystyle m^2=3^{2n}\)

Thank you!

 

[mathz]

:idea: Do you (or your kid) have a list of exponent properties at hand? :cool:

No.

 

[mmm4444bot]

If you have a textbook, be sure to check the index.

https://www.mathsisfun.com/algebra/exponent-laws.html

In the chart, symbols m and n can also represent algebraic expressions, like in your exercise. Remembering the patterns is helpful. :cool: