(^5 sqrt symbol a^6)/(^4 sqrt symbol a^3)
Is the answer 20sqrt symbol a^9
I've did the calculations, and I get
20sqrt symbol a^39
do you mean 20sqrt symbol a^9
^5 sqrt symbol a^6 = a^(6/5)
and ^4 sqrt symbol a^3 = a^(3/4)
a^(6/5)*a^(3/4) = a^((6/5)+(3/4))
= a^(39/20) = ^20sqrt symbol a^39
To simplify the given expression:
1. Start by simplifying each term within the radical separately.
The numerator, ^5√(a^6), can be written as (a^6)^(1/5). By applying the exponent rule, (a^6)^(1/5) is simplified to a^(6/5).
Similarly, the denominator, ^4√(a^3), can be written as (a^3)^(1/4), which simplifies to a^(3/4).
2. Divide the simplified numerator by the simplified denominator.
So, a^(6/5) ÷ a^(3/4) = a^(6/5 - 3/4).
3. To subtract the exponents, find a common denominator of 20 for the two fractions.
a^(6/5 - 3/4) = a^(24/20 - 15/20) = a^(9/20).
4. Finally, rewrite the expression as the fifth root of a raised to the power of 9/20.
The answer is ^5√(a^(9/20)), which can also be expressed as a^(9/20)^(1/5).
Note: It is important to be clear with the radical symbols. If you meant the entire expression to be under the radical (square root), please explicitly mention that.