Simplify:  4sqrt400/4sqrt80 Show your work.

4sqrt400/4sqrt5 = 4sqrt80
4sqrt80=4sqrt16 * 4sqrt5= 2*4sqrt5= 2^4sqrt5

Is this right ?

I'm not sure if that expression is 4*sqrt(400) / (4*sqrt(5)), or the fourth root (radical sign with a number four on it).

If it's the fourth root, then your answer is correct. `u`

To simplify the expression (4√400)/(4√80), you first need to find the square roots of 400 and 80, and then simplify the fraction.

√400 = 20, since 20 * 20 = 400.
√80 can be simplified by breaking it down into its prime factors: 2 * 2 * 2 * 2 * 5 = 2^4 * 5. Taking the square root of each factor gives you 2^2 * √5.

Now you can rewrite the expression as (4 * 20) / (4 * 2^2 * √5). The 4's in the numerator and denominator cancel each other out, leaving you with 20 / (2^2 * √5).

Finally, simplify 2^2 to 4, so the expression becomes 20 / (4 * √5), or 5 / √5. To simplify this further, multiply both the numerator and denominator by √5 to rationalize the denominator. This gives you (5 * √5) / (√5 * √5), which simplifies to (5√5) / 5.

The final simplified expression is √5, or the square root of 5.

So, your statement that 4√400/4√80 simplifies to 2^4√5 is not correct. The correct simplification is √5.