Question

Rewrite in simplest rational exponent form √x • 4√x. Please show each step of your process

Answer 1

Hey King! Is this what your problem looks like?\[\large\rm \sqrt{x}\cdot\sqrt[4]{x}\]

Answer 2

yes :)

Answer 3

When no number is written over the radical, it's implied that it's a 2.\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\]Square root = second root.
Ok so in general,\[\large\rm \sqrt[n]{x}=x^{1/n}\]We can rewrite our root as a rational exponent like this.
We get a fraction as an exponent.
The `denominator` is the degree of the root.

Answer 4

\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot \text{__}\]
So that's a way I could rewrite my first radical.
How bout the other one? :)
Any ideas?

Answer 5

would you reduce the second one to 2?

Answer 6

No.\[\LARGE\rm \sqrt[\color{orangered}{n}]{x}=x^{1/\color{orangered}{n}}\qquad\to\qquad \sqrt[\color{orangered}{4}]{x}=x^{1/\color{orangered}{4}}\]

Answer 7

\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot x^{1/4}\]

Answer 8

From here you need to apply one of your exponent rules:\[\large\rm \color{royalblue}{x^a\cdot x^b=x^{a+b}}\]

Answer 9

oh yeah sorry i was confused but I see how it's 1/4

Answer 10

@zepdrix is that it after that step ?

Answer 11

You need to apply the blue formula.
So you would have to add 1/2 and 1/4.

Answer 12

You'll need a common denominator to add those two fractions together.

Answer 13

the common denominator would be 2 right ?

Answer 14

@zepdrix

Answer 15

\[\large\rm \frac{1}{2}+\frac{1}{4}\]The common denominator is 4.
How do you turn the 2 into a 4?

Answer 16

multiplying it by 2

Answer 17

\[\large\rm \color{royalblue}{\frac{2}{2}}\cdot\frac{1}{2}+\frac{1}{4}\quad=\quad \frac{2}{4}+\frac{1}{4}\]Good good good.

Answer 18

wait when you said I had to apply one of the exponent rules what was it called?

Answer 19

It was the one that I colored in blue.
I think it's called the Exponent Addition Rule

Answer 20

something like that

Answer 21

the final answer simplified and all would be x^3/4 or am I wrong ?
@zepdrix

Answer 22

yay good job \c:/

Answer 23

thank you for the help. it was much needed