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:
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: