Problem #1

subtract. Express your answer in simplest form

(3x)/(18) minus (x)/(18)

MY steps:
(3x-x)/(18) = (2x)/(18)
and answer:
(2x)/(18)

Problem #18

write in simplest form.

(3x^5)/(15x^12)

My steps:

(3)/(15) = .60
x^5-12 = x^-7

so my answer is: .60x^-7

Problem #21

Add. express your answer in simplest form.

(x)/(6) + (3x)/(6)

= (x+3x)/(6)
my answer= (4x)/(6)

#1 : Yes, but one more step. You can take the 2 and the 18 and figure out how to reduce those. So it would be 1x/9 (Or just x/9)

#2: 3/15 = .2 On a technical level, .2x^-7 would be a correct answer. But not in its simplest form. 1/5 is the same as 3/15, so we can write it like:

1/5x^7

#3 One more step. What can you do with the 4 and 6? (Clue: Look at my reply to question #1 above)

my question is how is the answer

1/5x^7

if the exponent is a negative 7? and you have it as a positive 7

and for problem # 3

would then the last step be:

2x/3

4 1×4 2×2

10 1×10,2×5 in division

I apologize for the mistake in my previous response. You are correct - when reducing the expression (3x^5)/(15x^12) to its simplest form, the exponent should be negative.

To simplify (3x^5)/(15x^12), we can first simplify the coefficients 3 and 15:

3/15 can be reduced to 1/5 by dividing both the numerator and denominator by 3.

Next, we can simplify the variable terms x^5 and x^12 by subtracting the exponents:

x^5 - x^12 = x^(5-12) = x^(-7)

Putting it all together, the simplest form of (3x^5)/(15x^12) is:

(1/5)x^(-7)

As for problem #3, you correctly simplified (x/6) + (3x/6) as (4x/6). However, we can simplify the coefficient 4 and the denominator 6.

The largest common factor of 4 and 6 is 2. By dividing both the numerator and denominator by 2, we can further simplify the expression:

(4x/6) = (2/3)(2x/3)

Thus, the simplest form of (x/6) + (3x/6) is:

(2/3)(2x/3)