express a^8b^6c^7 whole root 4 in the simplest form??
To express (a^8b^6c^7)^(1/4) in the simplest form, we need to simplify the expression under the root and reduce the exponent.
Step 1: Simplify the expression under the root.
To simplify the expression, we divide each exponent by the root's index (4 in this case).
For 'a': 8/4 = 2
For 'b': 6/4 = 1.5
For 'c': 7/4 = 1.75
So, (a^8b^6c^7)^(1/4) simplifies to a^2b^(3/2)c^(7/4).
Step 2: Reduce the exponents.
Since 3/2 and 7/4 are fractions, we can try to write them with the same denominator, which is 4.
For 'b': 3/2 = 6/4
For 'c': 7/4 remains the same
Now, the expression becomes a^2b^(6/4)c^(7/4).
Step 3: Simplify the exponents and write the expression in the simplest form.
Simplifying the exponents gives us:
a^2b^(6/4)c^(7/4) = a^2b^(3/2)c^(7/4)
Finally, the expression (a^8b^6c^7)^(1/4) in simplest form is a^2b^(3/2)c^(7/4).