# [ASK] Exponents and Roots Simplification problem

• MHB
• Monoxdifly
In summary: Oh, well in that case, thank you for the compliment! I will try my best to avoid posting "bad" equations in the future. :)
Monoxdifly
MHB
The result of $$\displaystyle \frac{7x-\frac92\sqrt[6]{y^5}}{\left(x^{\frac56}-6y^{-\frac13}\right)x^{-2}}$$ for x = 4 and y = 27 is ...
a. $$\displaystyle \left(1+2\sqrt2\right)9\sqrt2$$
b. $$\displaystyle \left(1+2\sqrt2\right)9\sqrt3$$
c. $$\displaystyle \left(1+2\sqrt2\right)18\sqrt3$$
d. $$\displaystyle \left(1+2\sqrt2\right)27\sqrt2$$
e. $$\displaystyle \left(1+2\sqrt2\right)27\sqrt3$$

I got stuck at $$\displaystyle \frac{56-3^2\left(3^{\frac52}\right)}{2^-{\frac43}-2^{-2}}$$ and don't know how to continue to reach one of the options. By the way, don't you think that 7 is suspicious?

I simplified the original expression to $\dfrac{4(56-81\sqrt{3})}{\sqrt[3]{4}-1}$

Note evaluation of the original numerator ...

$28 - \frac{9}{2} \cdot 27^{5/6} \approx -42.1481$

evaluation of the denominator ...

$(4^{5/6} - 6\cdot 27^{-1/3}) \cdot \frac{1}{16} \approx 0.0734$

Division would yield a negative value. Clearly, all choices are positive. Maybe a typo or other error with the original expression?

skeeter said:
Division would yield a negative value. Clearly, all choices are positive. Maybe a typo or other error with the original expression?

According to you, what part of the question should be gotten rid of to reach one of the options?

Monoxdifly said:
According to you, what part of the question should be gotten rid of to reach one of the options?

Something is in error with the original expression. Could be an omission, a sign error, a coefficient error, an error in one or more exponents, or a combination of the aforementioned.

You can make an attempt to reverse engineer the original expression to fit one of the choices if you have the time and the inclination.

skeeter said:
You can make an attempt to reverse engineer the original expression to fit one of the choices if you have the time and the inclination.

I don't. Especially when I don't even know what's the supposed right answer. Not going to waste my time reverse-engineering up to five options. Gonna raise my white flag.

skeeter said:
I simplified the original expression to $\dfrac{4(56-81\sqrt{3})}{\sqrt[3]{4}-1}$
I can duplicate Skeeters answer. I wouldn't have had the patience to try simplifying the original expression if Skeeter hadn't already given the answer. It was very tedious and I had to go over it several times to correct mistakes. They must make software to do this.

Mr.Fly, you posted a "bad" expression, obviously.

Go stand in the corner for y minutes...

Monoxdifly said:
By the way, don't you think that 7 is suspicious?
Well, if that 7 was 20, then you'd be "in the range", with result = ~134.17,
between 3rd choice of ~119.36 and 4th choice of ~146.18.

Holy crappy!

So numerator: 7 * x * 9^(1/2) * y^(5/6)
denominator : [x^(5/4) - 6 * y^(-1/3)] * x^(1/2)

which matches the 5th choice...

Remind me not to look at any of your future equations :)

Wilmer said:
Remind me not to look at any of your future equations :)

Dude, that's harsh!

Monoxdifly said:
Dude, that's harsh!
No...no...I said that with my heart :)

## 1. 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, such as 53 where 5 is the base and 3 is the exponent.

## 2. How do you simplify an exponent expression?

To simplify an exponent expression, you can use the rules of exponents. For example, when multiplying two numbers with the same base, you can add the exponents. When dividing two numbers with the same base, you can subtract the exponents. You can also use the power rule, which states that when raising a power to another power, you can multiply the exponents.

## 3. What is a root?

A root is the inverse operation of an exponent. It is a number that, when raised to a certain power, gives the original number. For example, the square root of 25 is 5, because 52 equals 25.

## 4. How do you simplify a root expression?

To simplify a root expression, you can use the rules of roots. For example, when multiplying two numbers with the same root, you can add the exponents. When dividing two numbers with the same root, you can subtract the exponents. You can also use the power rule, which states that when taking the root of a power, you can divide the exponent by the root.

## 5. What is the difference between an exponent and a root?

An exponent represents repeated multiplication of a base number, while a root represents the inverse operation of an exponent. An exponent is written as a superscript, while a root is written as a radical symbol.

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