Question

Which of the following algebraic expressions represents the verbal expression given below?

The opposite of a number, raised to the fourth power, is divided by five.

Answer 1

of a number =x

opposite is just -

so we start with a -x

Answer 2

-x is raised to the 4th power....can you tell me what it's going to look like now?

Answer 3

hint: it has to do with exponents

Answer 4

http://media.education2020.com/evresources/2003-01-03-00-00_files/i0150000.jpg

Answer 5

?

Answer 6

yes that looks about right. good job

Answer 7

thanks

Answer 8

Wait. There is a mistake.

Answer 9

explain

Answer 10

?

Answer 11

You need to be careful with the square of -x.

There is a difference between \(-x^2\) and \( (-x)^2\).

\( -x^2\) means take the square of x, then find its opposite.

\((-x)^2 \) means find the opposite of x, then square it.

Answer 12

Well it doesnt matter in this case because the exponent value is positive.

Answer 13

Here is an example:
Let's say x = 4.

\(-x^2 \) means: square x: \(4^2 = 16\);
now find its opposite: the opposite of 16 is -16. The answer is -16

\( (-x)^2 \) means find the opposite of x. The opposite of 4 is -4.
Now square it. The square of -4 is (-4)(-4) = 16. The answer is 16.

As you can see, one expression gives you -16 , and the other one gives you 16.

Answer 14

I see, can you write a verbal expression for the other expression then to compare.

Answer 15

so what would the anser look like?

Answer 16

Let's take your problem from the beginning.

The opposite of a number, raised to the fourth power, is divided by five.

A number: x

The opposite of a number: -x

raised to the fourth power: \( (-x)^4 \)

is divided by five. \( \dfrac{(-x)^4}{5} \)

This is your final answer.

Answer 17

Great question.

\( - \dfrac{x^4}{5} \)

A number raised to the 4th power is divided by five. Then the opposite is taken.

Answer 18

@mathstudent55 Great job! I did it so fast I forgot about this!

Answer 19

thanks both of you for the help! :)

Answer 20

wlcm