Question

Choose the correct simplification of the expression the quantity a to the 3rd power over b to the 7th power all raised to the 2nd power
a to the 5th power over b to the 9th power

a over b to the 14th power

a to the 6th power over b to the 14th power

a6b14

Answer 1

\[\large (\frac{ a^3 }{ b^7 })^2\]

Like that?

Answer 2

yes

Answer 3

So when the exponents are separated by the parenthesis...you multiply...and you apply it to each term...so

\[\large (\frac{ a^3 }{ b^7 })^2 = \frac{ a^{3 \times 2} }{ b ^{7 \times 2} } = \frac{ a^{?} }{ b^{?} }\]

Answer 4

a6 and b14

Answer 5

Right...just keep it as a fraction though...nothing changes in that sense...so we have:

a to the 6th power over b to the 14th power

Answer 6

cool thanks can you help one more time lol

Answer 7

Sure :)

Answer 8

on this this.
[7.04] Choose the correct simplification of the expression a to the 12th power times b to the 8th power all over a to the 2nd power times b to the 4th power.

a10b4

a6b2

1 over a to the 10th power times b to the 4th power

1 over a to the 14th power times b to the 12th power

Answer 9

\[\large \frac{ a^{12} \times b^8 }{ a^2 \times b^4 }\]

Like that I'm assuming...

Answer 10

A96 and B8 but that's not right

Answer 11

When you are dividing exponents with the same base...you subtract the exponents and leave the base alone...so

\[\large \frac{ a^{12}b^8 }{ a^2b^4 } = a^{12 - 2} \times b^{8 - 4} = a^{?}b^{?}\]

Answer 12

A 10 B 4

Answer 13

Good! Which is answer choice...?

Answer 14

it be A right

Answer 15

That would be correct!

Answer 16

cool thanks you um can you still help me?????

Answer 17

Yeah sure if I can :)...and sorry was helping someone else

Answer 18

its ok.

[7.06] Choose the correct simplification of the expression −4x2(6x − 5x2 − 5).

20x4 + 24x3 + 20x2

−9x4 + 2x3 − 9x2

20x4 − 24x3 + 20x2

−20x4 + 24x3 − 20x2

Answer 19

So for this one...we take the term outside the parenthesis...(-4x^2) and multiply it by EVERY term INSIDE the parenthesis

\[\large -4x^2 \times 6x = \space ?\]
\[\large -4x^2 \times -5x^2 = \space ?\]
\[\large -4x^2 \times -5 = \space ?\]

Answer 20

20x4 − 24x3 + 20x2

it be this one right

Answer 21

That would be correct! Good work!

Answer 22

thanks you can you help on this one too

[7.07] Choose the correct product of (5x + 4)2.

25x2 + 40x + 16

25x2 − 16

25x2 + 16

25x2 − 40x + 16

Answer 23

I think it will be this one but not sure lol = 25x^2 +40x +16

Answer 24

You are correct again! Pfft and you said you needed help :P

Answer 25

will yea i am not good at math lol.

[7.01]

Choose the polynomial that is written in standard form.

xy3 + 4x5y + 10x3

x4y2 + 4x2y + 8x

−9x4y2 + 4x3y5 + 10x2

x6y3 + 4x4y8 + x2

Answer 26

What do you think it is first...?

Answer 27

this one lol x^4y^2 + 4x^2y + 8x

Answer 28

Once again Correct! :)

Answer 29

wow i am good for once in math lol

[7.04] Choose the correct simplification of the expression (−9a3b2c10)0.

0

9a3b2c10

1

−9

Answer 30

Haha idk I think you were lying and are like some prodigy haha :)

Your answer to this one is...?

Answer 31

will it be 0 lol

Answer 32

HA finally I can help :P what is ANYTHING raised to the 0 power...?

Answer 33

be 1

Answer 34

right....then your answer is?

Answer 35

1 b/c If exponent is zero then the answer will always be one

Answer 36

That is correct in this case..because the 0 is outside the parenthesis so it gets applied to every term inside...so yes in this case...1

Answer 37

cool help me on this b/c i don't know this one lol

[7.08] Find the quotient of the quantity 21 times x to the 2nd power times y to the 6th power plus 6 times x times y to the 3rd power minus 30 times x times y all over 3 times x times y.

21x2y6 + 6xy3 − 10

7xy5 + 2y2 + 10

7xy5 + 2y2 − 10

7xy5 + 2y − 10

Answer 38

\[\large \frac{ 21x^2y^6 + 6xy^3 - 30xy}{ 3xy }\]

Okay...this can just be broken up.....what is

\[\large \frac{ 21x^2y^6 }{ 3xy } = \space ?\]

Answer 39

7xy5+2y2-10

Answer 40

-_- yeah...you're a prodigy :P lol good work!

Answer 41

thank you lol.

[7.03] Identify the Exponent Law shown in the example below.

x2x4 = x2+4 = x6

None of the choices below are correct.

Power of a Product

Power of a Power

Product of Powers

Answer 42

will it be this one Power of a product becuase your multiplying x^2 by x^4. But the powers add. Product of powers would be multiplying the powers. So x^2 by x^4 would be x^8

Answer 43

No this would be the product of powers rule...because you are starting with a product....but adding the powers....the power of a product would be something like

(2x)^2

power of a power is something like

(2x^2)^2

and the product of powers is this one

Answer 44

oh ok.

[7.08] Find the quotient of the quantity negative 12 times x to the 3rd power plus 21 times x to the 2nd power minus 6 times x all over negative 3 times x.

−4x2 − 7x + 18

4x2 + 7x + 18

−12x3 + 21x2 + 2

4x2 − 7x + 2

Answer 45

mmhmm tell me the answer genius :P

Answer 46

be this one −12x3 + 21x2 + 2 i am not sure lol

Answer 47

\[\large \frac{ -12x^3 + 21x^2 - 6x }{ -3x }\]

what is

\[\large \frac{ -12x^3 }{ -3x } = \space ?\]

Answer 48

i don't know

Answer 49

What is -12 divided by -3?

Answer 50

4

Answer 51

mmhmm...and what is x^3/x ? Remember when dividing exponents...you subtract themm...so x^3/x = x^(3 - 1) = x^?

Answer 52

be this one 4x2 + 7x + 18 right

Answer 53

So close...but no

the next step would be

\[\large \frac{ 21x^2 }{ -3x }\]

21 / -3 = ?

Answer 54

7

Answer 55

.....is it 7? remember you are dividing a positive by a negative....

Answer 56

−4x2 − 7x + 18

Answer 57

When did the 4x^2 become a negative? that's not right either...

Answer 58

so far we have

4x² - 7x ....which one looks like that?

Answer 59

4x2 − 7x + 2

Answer 60

There we go...you didn't seem too sure on that one...did you get it?

Answer 61

yes i get it now. how about this one

[7.04] Choose the correct simplification of the expression 4 times b all over a to the power of negative 10.

a to the 10th power times b all over 4

4a10b

4 over a to the 10th power times b

Already simplified

Answer 62

will it be this one Already simplified

Answer 63

Not quite...we dont like negative exponents in the denominator...

To make it positive...we simply make it go from the denominator...to the numerator...so we will have 4a^10b

Answer 64

so it's B then??????

Answer 65

That would be correct :)

Answer 66

cool :) [7.03] Choose the correct simplification of the expression (2x7y)2(y5)3.

4x7y10

4x9y10

4x14y16

4x14y17

Answer 67

I think it will be 4x^14 y ^17?

Answer 68

Perfect!

Answer 69

cool lol how about this one and i don't know how to do it Question 20 (Essay Worth 5 points)

[7.02] Find the difference of (−5x2 − 4x3 − 3) − (9x3 + 3x − 8x2). Be sure to show all of your work in a neat and organized fashion.

Use the ^ (shift 6) symbol to show an exponent. For example, x squared can be written as x^2.

Answer 70

will be this Find the quotient of the quantity negative 5 times x to the 3rd power plus 20 times x to the 2nd power minus 25 times x all over negative 5 times x.

(-5x^3+20x^2-25x)/(-5x)=
x^2-4x+5

Answer 71

Or this one First, convert the right side, since there's a negative sign in front of it. so it's -9x^3-3x+8x^2
Then put the whole expression into one long string:
-5x^2-4x^3-3-9x^3-3x+8x^2

then start combing like terms:

3x^2 - 13x^3 - 3x -3 i am not sure lol

Answer 72

Okay....so for the "difference" one you posted...

(-5x^2 - 4x^3 - 3) - (9x^3 + 3x - 8x^2)

What we do first...is distribute the '-' sign through the 2nd parenthesis....

-5x^2 - 4x^3 - 3 -9x^3 - 3x + 8x^2

Now we just combine like terms...

-4x^3 - 9x^3 - 5x^2 + 8x^2 - 3x - 3

-4x^3 - 9x^3 = -13x^3
-5x^2 + 8x^2 = 3x^2

so we have

-13x^3 + 3x^2 - 3x - 3

Answer 73

The one you JUST posted is exactly what I just did

Answer 74

lol that's funny lol :)

Answer 75

haha so that would be correct :)

Answer 76

All done now? :)