# Math Help - Express radicals in exponential form.

1. ## Express radicals in exponential form.

Hi guys,

the task: Express each radical in exponential form. Simplify using the exponent laws when possible.

1. root of k^2/3

= (k^2/3)^1/2

= and then?

2. root of ab^2

= (a)^1/2 (b^2)^1/2

= a^1/2 b^1

3. 4 root of 81 x^8 y^12

= (81)^1/4 (x^8)^1/4 (y^12)^1/4

= 81^1/4 x^2 y^3

4. cube root of x and square root of x

= (x)^1/3 (x)^1/2

= x^2/6+3/6

= x^5/6

Is that right or not? Explain please. Thanks.

2. ## Re: Express radicals in exponential form.

Originally Posted by ford2008
the task: Express each radical in exponential form. Simplify using the exponent laws when possible.

1. root of k^2/3

= (k^2/3)^1/2

= and then?

2. root of ab^2

= (a)^1/2 (b^2)^1/2

= a^1/2 b^1

3. 4 root of 81 x^8 y^12

= (81)^1/4 (x^8)^1/4 (y^12)^1/4

= 81^1/4 x^2 y^3

4. cube root of x and square root of x

= (x)^1/3 (x)^1/2

= x^2/6+3/6

= x^5/6

Is that right or not? Explain please. Thanks.
Why in the world don’t you learn basic LaTeX?
1) [TEX]\sqrt[3]{k^2} [/TEX] gives $\sqrt[3]{k^2}$

2) [TEX]\sqrt{ab^2} [/TEX] gives $\sqrt{ab^2}$

3) [TEX]\sqrt[4]{81x^8y^{12}} [/TEX] gives $\sqrt[4]{81x^8y^{12}}$

4) [TEX]\sqrt[3]{x\sqrt{x}} [/TEX] gives $\sqrt[3]{x\sqrt{x}}$

3. ## Re: Express radicals in exponential form.

Hey Plato,

I will learn basic LaTeX. Had no time yet to start.
Your No. 1 should be just a square root of k^2/3 not a cube root.

So could you tell me if my answers are right or whats wrong?

4. ## Re: Express radicals in exponential form.

Originally Posted by ford2008
Your No. 1 should be just a square root of k^2/3 not a cube root.
So could you tell me if my answers are right or whats wrong?
That may be your whole problem! You do not understand the notation.

$k^{\frac{2}{3}}=\sqrt[3]{k^2}$. Thus it is a cube root.

For any fractional exponent $k^{\frac{M}{N}}=\sqrt[N]{k^M}$.

5. ## Re: Express radicals in exponential form.

Thank you. I think I got it now.