Express the result in the simplest form 4 root a^8b^6c^7
To express the expression 4√(a^8b^6c^7) in its simplest form, we can begin by breaking down the expression under the radical sign. Remember that taking the root of a number or variable is the same as raising it to the power of 1/n.
First, let's separate the variables and simplify the expression:
4√(a^8b^6c^7) = 4√(a^8) * √(b^6) * √(c^7)
Next, simplify the roots of the variables:
4√(a^8) = 4 * a^(8/2) = 4a^4
√(b^6) = b^(6/2) = b^3
√(c^7) = c^(7/2)
Now, we can simplify the expression further by multiplying the simplified variables inside and outside the radical:
4a^4 * b^3 * c^(7/2)
Therefore, the expression 4√(a^8b^6c^7) in its simplest form is 4a^4 * b^3 * c^(7/2).
To express the given expression, 4√(a^8b^6c^7), in the simplest form, we need to simplify the expression under the square root.
Let's break down each term:
a^8 can be simplified as (a^4)^2, since the exponent 8 can be split into 4 * 2. As a result, we have 4√((a^4)^2).
b^6 can be simplified as (b^3)^2, using the same logic. So we now have 4√((a^4)^2(b^3)^2).
c^7 cannot be simplified any further since the exponent is not divisible by any smaller whole numbers.
Now, let's simplify each term under the square root:
√(a^4)^2 is equivalent to multiplying the exponent inside the square root by the exponent outside, which gives us a^4.
√(b^3)^2 is similar, resulting in b^3.
c^7 stays the same.
Combining all the simplified terms, we get the simplest form of the expression: 4a^4b^3c^7.
divide all the powers by 2.
leave any leftovers inside the root.
that is, √n^7 = n^3 √n ...