Math help Please help Thank you?

Question

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

Answer 1

fourth root of x^3 times seventh root of x^11 = ?
Using rational exponents we write:
x^3/4 * x^11/7 = x^ (21/28 + 44/28) = x^65/28.

Using rads we would write:
fourth root of x^3 times seventh root of x^11
= 28th root of x^21 * 28th root of x^44
= 28th root of x^65
This second method is much more confusing and easire to make errs.

Answer 2

I suppose it's better for an equation that has several exponential components. For example,
5 = sqrt(x)*(x^3) is easier to solve if you change the radical symbol (in this case sqrt), to 5 = (x^1/2)*(x^3).
It's just easier on the eyes to see that this is 5 = (x^3/2),
so x = 5^(2/3)

Answer 3

In derivitives, you need to subtract 1 from the exponent, so it can't be a radical

ex. derivitive of sqrt x = d((x)^(1/2)) = (1/2) x^(-1/2)
can't do that with radicals

Answer 4

cube root of x^5 times fifth root of x^3 =
x^(5/3) • x^(3/5) = x^(5/3 + 3/5) =
x^(34/15) = x² • x^(4/15) =
x² times 15th root of x^4.

Answer 5

There are legal operatins you can do on exponents

for instance x^3/x^0.5 = x^2.5

using root symbol result should be x^2 * sqr(x)