simplify:

[fourth root(a^6)]-[2a(square root(a))]
when a is greater than 0

solution: -a times(square root(a))

please explain thanks!

To simplify the expression [fourth root(a^6)] - [2a(square root(a))], we can break it down into smaller parts and simplify each part individually.

Let's start with the fourth root part: [fourth root(a^6)]. The fourth root of a number is the same as raising the number to the power of 1/4. So, [fourth root(a^6)] can be rewritten as (a^6)^(1/4). Applying the property of exponents, we can multiply the exponents, giving us a^(6/4) or a^(3/2).

Now let's simplify the second part: [2a(square root(a))]. We can simplify this by multiplying the coefficients and combining the like terms inside the parentheses. So, 2a(square root(a)) becomes 2a * square root(a), which simplifies to 2a(square root(a)).

Now we can rewrite the original expression with our simplified parts:

[a^(3/2)] - [2a(square root(a))]

To combine these parts, we need a common base for the exponent of a. Since the exponent of the first term is 3/2 and the exponent of the second term is 1, we need to rewrite the second term with a^(3/2) as well.

So, [a^(3/2)] - [2a(square root(a))] becomes [a^(3/2)] - [2a(a^(1/2))].

Now, we can simplify further by combining the like terms: [a^(3/2)] - [2a(a^(1/2))] can be rewritten as [a^(3/2)] - [2a^(3/2)]. Notice that the bases are the same (a^(3/2)), so we can subtract the coefficients: 1 - 2, which gives us -1.

Finally, we can rewrite the simplified expression: -1 * a^(3/2) or -a * a^(1/2) which is equal to -a * square root(a).