Please help! I need to simplify this and am confused.
(sqrt5 a^7/2)^4 a^3/a^8
It would help if you posted the equation more clearly by using parentheses.
In general, though use order of operations and exponential rules to reduce the # of variables & constants. For example, a^3/a^8 would become 1/a^5, because when you divide you subtract the exponents.
See http://www.jiskha.com/display.cgi?id=1245905705
To simplify the expression (sqrt(5) a^(7/2))^4 * (a^3/a^8), we can follow these steps:
Step 1: Simplify the expression inside the parentheses first.
In this case, we have (sqrt(5) a^(7/2))^4. To simplify this, we raise both the square root and the exponent by 4:
(sqrt(5))^4 * (a^((7/2)*4))
Simplifying further, we get:
5^2 * a^((7/2)*4)
25 * a^7
Step 2: Simplify the other part of the expression, which is a^3/a^8.
To divide two numbers with the same base (in this case, a), we subtract the exponents:
a^(3-8)
a^(-5)
Step 3: Combine the simplified expressions from Step 1 and Step 2:
(25 * a^7) * (a^(-5))
Step 4: Multiply the coefficients (numbers) and combine the variables (a) using the exponent rule of addition:
25 * a^(7+(-5))
25 * a^2
Therefore, the simplified expression is 25a^2.