How do you simplify the following?
1) (25^(2t))/(125^t)
2) (3^(x+3)-3^(x+1))/2^2
1)
2)
4 Answers
-
5^t -
3^(x + 1) xx 2
Explanation:
25^(2t)/(125^t)
Simplify to the least term;
Recall;
Therefore;
(3^(x + 3) - 3^(x + 1))/2^2
Recall;
Therefore;
Can also be;
Factorizing out the common terms
Remember;
Hence;
Explanation:
https://www.youtube.com/watch?v=ARLS2TmFT94
Explanation:
"using the "color(blue)"laws of exponents"
•color(white)(x)a^mxxa^n=a^((m+n))
•color(white)(x)a^m/a^n=a^((m-n))" and "(a^m)^n=a^(mn)
(1)
(25^(2t))/(125^t)
=((5)^2)^(2t)/((5)^3)^t
=(5)^(4t)/5^(3t)=5^((4t-3t))=5^t
(2)
=(3^x(3^3-3^1))/4
=(3^x(27-3))/4
=(cancel(24)^6(3^x))/cancel(4)^1=6(3)^x
-
5^t -
2 xx 3^(x+1)
Explanation:
For Question 1:
By Exponential law:
So no we have:
Therefore:
For Question 2:
First, lets simplify the numerator:
By Exponential Law:
So,
We now have:
Factor out the common term
And now we have: