1-4. Are the following results correct?  Simplify. Assume a, x , and y are not zero. 1. 8x/12 = 1x/3 (8*1,8*3) 2. 15a^3/25a = 3a^3/5a (3a^3*5, 5a*5) 3. 10^3/10^2 = 10 (10^3-2) 4. -x^2y/(-x^2)^2...

1-4. Are the following results correct?

 

Simplify. Assume a, x , and y are not zero.

1. 8x/12 = 1x/3 (8*1,8*3)

2. 15a^3/25a = 3a^3/5a (3a^3*5, 5a*5)

3. 10^3/10^2 = 10 (10^3-2)

4. -x^2y/(-x^2)^2 y^2 = I couldn't figure this one out, so I would like some help in the explanation of this problem.

Asked on by anya4one

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samhouston | Middle School Teacher | (Level 1) Associate Educator

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#3 correct.  Here are the explanations of the problems.

 

1.  8x/12 can be simplified by 4. 

8x `-:` 4 = 2x 

12 `-:` 4 = 3

The correct answer is 2x/3.

 

2.  15a^3 / 25a can be simplified by 5. 

15a^3 `-:` 5 = 3a^3

25a = 5a

3a^3 / 5a can be simplified using exponential laws.  When dividing powers, you subtract the exponents.  Note that 5a is actually 5a^1.

a^3 - a^1 = a^2

A positive exponent places the variable in the numerator.

The correct answer is 3a^2 / 5. 

 

3.  10^3 / 10^2

10^(3-2)

10^1

10

The correct answer is 10.

 

4.  -x^2y/(-x^2)^2y^2

For problems with multiple variables, I recommend dealing with one variable at a time and then combining them at the end.

You must first work the parentheses according to order of operations.

(-x^2)^2

To find the power of a power, you multiply the exponents.

-x^(2*2) = -x^4

So now (just dealing with the variable x), we have...

-x^2 / -x^4

First of all, the negatives cancel, so now we have...

x^2 / x^4 = x^(2-4) = x^(-2)

Because the exponent is negative, x^2 will go in the denominator in the final answer.  Now lets work with the variable y.

y / 2y^2

To make things easier, give y a coefficient and exponent of 1.

1y^1 / 2y^2

Set aside the constants (numbers).  The final fraction will contain 1 / 2.

y^1 / y^2 = y^(1-2) = y^-1

Because the exponent is negative, y^1 (or simply just y) will go in the denominator of the final answer.

Now we bring the answer together.

We have the fraction 1/2.

We know that x^2 is in the denominator.

We know that y is in the denominator.

The correct answer is 1 / (2x^2 * y).

 

Just as a review, here are the basic exponentials laws:

n^a * n^b = n^(a+b)

n^a `-:` n^b = n^(a-b)

(n^a)^b = n^(a*b)

n^-a = 1 / n^a

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