Express each of the following radical expression using fractional exponents?

Question

1.4(sqrt x^3)
2.(sqrt t)
3.4(sqrt x^7)
4 1/5(sqrt x^2)

Answer 1

square root expressed as a fraction is 1/2
when you want to take the square root of a number raised to a power, you just multiply the power by 1/2

so the answers are:

1. 4(x)^3/2
2. t^1/2
3. 4(x)^7/2
4. 1/5(x)^1 or just (1/5)x

Answer 2

Hi,
When we convert radical expressions to fractional exponents, the index (2 for square root, 3 for cube, etc) of the radical becomes the denominator of the fraction. So, let’s do your problems using this idea.

1) 4√(x3)
=4x^(3/2) (If this had been the fourth root of x^2, it would have been x^(3/4)).
2) √(t)
= t^(1/2)
3) 4√(x^7)
= 4x^(7/2)
4) √1/5√(x²)
= (1/5)x^(2/2)
=(1/5)x

FE

Answer 3

1. 4 x^(3/2)
2. T^(1/2)
3. 4 x^(7/2)
4. 1/5(x), since sqrt and sqr cancel out. You can expresss this as x^ (2/2) or x^1, which is simply x.
An alternate answer here is 1/(5x), if the original expression is 1 / (5√x^2).

Answer 4

sqrt have a fraction power with a denominator of 2
cube roots have a fraction power with a denom of 3
etc.

4 sqrt x^3 = 4x^(3/2)
sqrt t = t^(1/2)

you do the rest

Answer 5

you multiply the coefficients at the front and at the indices. So it's 15 x ^ 13/20