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

my answer:

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

= and then?

2. root of ab^2

my answer:

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

= a^1/2 b^1

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

my answer:

= (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

my answer:

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

= x^2/6+3/6

= x^5/6

Is that right or not? Explain please. Thanks.

Re: Express radicals in exponential form.

Quote:

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

my answer:

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

= and then?

2. root of ab^2

my answer:

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

= a^1/2 b^1

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

my answer:

= (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

my answer:

= (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 $\displaystyle \sqrt[3]{k^2}$

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

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

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

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?

Re: Express radicals in exponential form.

Quote:

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.**

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

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

Re: Express radicals in exponential form.

Thank you. I think I got it now.