Expanding Exponent Expressions

In summary, the conversation was about simplifying the expression 3x\sqrt{3x-1}. The summary includes the equation that the expression is equal to, 12x^{2} - 4x, and the alternate form that can be written as 3x(3x-1)^{\frac{1}{2}}. The conversation then moves on to simplifying a more complex expression, x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}, which can be simplified to \frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1
  • #1
thomas49th
655
0
Hi, I don know how to go about expanding things such as

[tex]3x\sqrt{3x-1}[/tex]
apparently that equals 12x^{2} - 4x

i know that [tex]3x\sqrt{3x-1}[/tex] can be written as [tex]3x(3x-1)^{\frac{1}{2}}[/tex]

but i don't know what to do. I can't remeber.

Thanks :)
 
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  • #2
[tex]3x\sqrt{3x-1} \neq 12x^2 - 4x[/tex]
 
  • #3
SORRY MY BAD I MENT [tex]2x\sqrt{3x-1}[/tex] = 12x^{2} - 4x

How do i get there?

Thanks :)
 
  • #4
[tex]2x\sqrt{3x-1} \neq 12x^2 - 4x[/tex]
 
  • #5
SORRY. Ill start a bit further back
i have this:

[tex]x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}[/tex]

and I don't know how it simplifies to

[tex]\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}[/tex]I can't see that the
[tex]x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}} [/tex] will equal [tex]\frac{3x^{2}}{2\sqrt{3x-1}}[/tex]

but i can't see how the other bit simplifies... can you show me

Thanks
 
Last edited:
  • #6
thomas49th said:
SORRY. Ill start a bit further back
i have this:

[tex]x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}[/tex]

and I don't know how it simplifies to

[tex]\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}[/tex]

I can't see that the
[tex]x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}} [/tex] will equal [tex]\frac{3x^{2}}{2\sqrt{3x-1}}[/tex]

Hi thomas49th! :smile:

Do you follow:
[tex]\frac{3x^{2}}{2\sqrt{3x-1}}\,+\,2x\sqrt{3x-1}[/tex]

[tex]= \frac{3x^{2}}{2\sqrt{3x-1}}\,+\,\frac{2x(3x-1)}{\sqrt{3x-1}}[/tex] ? :smile:
 
  • #7
yes i can see a common denomitor so u multiply both the numerator and demonitor by [tex]2\sqrt{3x-1}[/tex] of the fraction
Cheerz :)
 

What is an exponent?

An exponent is a number that represents how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number.

What does it mean to expand an exponent expression?

Expanding an exponent expression means to write it as a series of multiplications, using the exponent to indicate the number of times the base number is multiplied by itself.

How do you expand an exponent expression?

To expand an exponent expression, you can use the exponent rule which states that for any non-zero number a and positive integers m and n, am x an = am+n. This means that when multiplying two numbers with the same base, you can add their exponents together.

Can you give an example of expanding an exponent expression?

Sure, for example, to expand (23)4, you can use the exponent rule to rewrite it as 23 x 4 = 212. This means that (23)4 is equal to 2 multiplied by itself 12 times.

Why is it important to understand how to expand exponent expressions?

Understanding how to expand exponent expressions is important because it allows us to simplify and solve more complex mathematical equations involving exponents. It also helps us to better understand the properties and operations of exponents.

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