Solve equations with Radicals and exponents?

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

Any time solving an equation involves manipulation of the exponent of a term, it's helpful to have an exponent instead of a radical. For example, if a term is being cubed, you need to triple the exponent. If the term contains a radical, it's easier to see how to do that if it's being raised to the fractional exponent instead. The same goes if several radicals with the same argument, or powers of the same argument, are being multiplied together, because you can just sum the fractional exponents.

Answer 2

the square root of the cube of 64 would imply that you to cube 64 and then take the square root, very large numbers.
in exponent form 64^(3/2) you can arrange the the exponents in any order so it would be more practical to take the square root of 64, 8, and then cube that.

here's another example
the square root of 64 equals the cube of x
this is easier if you write it
64^(1/2)=x^3
then take both sides to the (1/3) power
64^(1/6)=x=2

Answer 3

Rational exponents defintely make taking first derivatives and first integrals much easier.

Answer 4

2?(x-2)^2=50 (2 ?(x-2)^2)^3=50^3 8 ?(x-2)^6=125000 8(x+2)^2=125000 8(x^2+4x+4)=125000 8x^2+32x+32=125000 8x^2+32x+32-125000=0 8x^2+32x-124968=0 8 (x-123) (x+127) = 0 x=-127 x=123 x=-127, 123 answer//