Hi I need some help. I'm stuck on this equation. I don't know where to start tbh. A step by step answer would be great.
#Help with equation.
neon bear
high trailBOT
royal crown
I would start by factoring out the constants 256 and 64. Once you do that you'll only have $(x^3x^{1/2})^{1/4}/x^{4/5}$ left. Think about what happens when you multiply and divide those variables and how the exponent changes along with it.
uncut pecanBOT
Darin__
royal crown
$$\frac{\sqrt[4]{x^3x^{\frac{1}{2}}}}{\sqrt[5]{x^4}}$$
uncut pecanBOT
Darin__
neon bear
Sorry I'm just trying to get my head around that answer
royal crown
It's alright, let's take care of the easy part first
What is the fourth root of 256 and what is the fifth root of 64? Or in other words what is a and b when $a^4=256$ and $b^5=64$
uncut pecanBOT
Darin__
royal crown
Yeah that's true but we're looking at fourth and fifth roots here, not square roots.
So it's $aaaa=256$ and $bbbbb=64$, your answer would be right if it was only $aa=256$.
uncut pecanBOT
Darin__
royal crown
Yeah, and sorry I just realized the fifth root of 64 doesn't give a whole number so we can just leave it at $\sqrt[5]{64}$
uncut pecanBOT
Darin__
royal crown
Now that we have that out of the way, think about what happens when you multiply $x^3$ and $x^\frac{1}{2}$
uncut pecanBOT
Darin__
royal crown
?
When exponents multiply they add, that way you can combine the two x's into one
So $x^3*x^\frac{1}{2}=x^{3+\frac{1}{2}}$
uncut pecanBOT
Darin__
royal crown
Does that make sense
neon bear
Ohh okay yeah makes sense
royal crown
So next thing, we can say $\sqrt[4]{x}=x^\frac{1}{4}$
uncut pecanBOT
Darin__
royal crown
And also remember when you raise something by an exponent which in this case we're raising x by the 1/4 exponent, you can multiply the exponents.
So you get $(x^\frac{7}{2})^\frac{1}{4}=x^{\frac{7}{2}*\frac{1}{4}}$
uncut pecanBOT
Darin__
royal crown
We have 7/2 because that's 3+1/2, if you were confused where that comes from
neon bear
Yeah got it ☺️
royal crown
Now do the same thing on the bottom, with the $(x^4)^\frac{1}{5}$
uncut pecanBOT
Darin__
royal crown
And the final step is when you divide two x's raised to some exponent, you subtract the exponents, similar to how when you multiply two x's you add the exponents
So the top is $x^\frac{7}{8}$ and bottom is $x^\frac{4}{5}$ right? Now when you divide the two you subtract the exponents and end up with some number
uncut pecanBOT
Darin__
royal crown
So that is your simplified x and just bring your constant from before, $\frac{4}{\sqrt[5]{64}}$ and multiply by your simplified x and that should be your final answer
uncut pecanBOT
Darin__
royal crown
That is the goal of this question correct? simplify the expression down
neon bear
Will do! Thanks alot