Please simplify: Very confused, have many problems like this and need some guidence. Thanks!
(root5a^7/2)^4 a^3/a^8
The problem has been solved before. See following link for explanations.
http://www.jiskha.com/display.cgi?id=1245905705
I have added the following clarification for Carmin. It is reproduced here in case you are also interested.
...
=(sqrt(5)4*(a(7/2))4) a3-8
=5(1/2)*4*a(7/2)*4*a3-8
=25 a14 a-5
=25 a9
the denominator 2 in the fraction (7/2) is an exponent and not a simple number. This is probably from where you got the 16.
So the 16 is not part of the answer? It's just 25 a^9?
Right!
To simplify the given expression (root5a^7/2)^4 a^3/a^8, we can follow these steps:
Step 1: Simplify the inside of the first parentheses.
Inside the parentheses, we have root(5a^7/2). To simplify this, we can rewrite it as (5a^7/2)^(1/2).
Step 2: Simplify the exponent inside the first parentheses.
The exponent inside the first parentheses is 1/2, which means we can take the square root of the expression (5a^7/2). So, the first parentheses simplifies to √(5a^7/2).
Step 3: Apply the exponent outside the parentheses.
Now, we raise the expression √(5a^7/2) to the power of 4. This gives us (√(5a^7/2))^4.
Step 4: Simplify the inside of the second parentheses.
Inside the second parentheses, we have a^3 divided by a^8. To simplify this, we can subtract the exponents since the base (a) is the same. This gives us a^(3-8), which simplifies to a^(-5).
Step 5: Combine the simplified expressions.
Now, we can combine the expressions (√(5a^7/2))^4 and a^(-5) by multiplying their exponents. This gives us (√(5a^7/2))^4 * a^(-5).
In conclusion, the simplified form of the given expression (root5a^7/2)^4 a^3/a^8 is (√(5a^7/2))^4 * a^(-5).