Question

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

a2a3 = a2+3 = a5

Power of a Product

Power of a Power

Product of Powers

None of the Above

Answer 1

Product of powers. It is \[(a^2)*(a^3)\]

Answer 2

Thank You I will let you know if this is correct. Please dont leave yet

Answer 3

If you say so.

Answer 4

[7.03] Choose the correct simplification of the expression (5x4y2z2)(3x4y3z5).

15x16y6z10

15x8y5z7

8x8y5z7

8x16y6z10

Answer 5

\[15x^8y^5z^7\]

Answer 6

Just combine the constants in front and then add the exponents.

Answer 7

Ohhh. Okay i have a few more if thats ok

Answer 8

@Nurali Try to explain the answer, not just give it.

Answer 9

I'm kinda getting the adding and subtracting . Just not the Multiplication and Division

Answer 10

Multiplication is adding the exponents, division is subtracting them. That's all.

Answer 11

Ohhh.

Answer 12

[7.03] Choose the correct simplification of the expression (7ab3)2.

49ab6

49a2b5

49a2b6

14a2b6

Answer 13

That's power to a power. Since you're raising the ENTIRE thing to a power. Think of it like this:

Answer 14

\[(7ab^3)(7ab^3)\]

Answer 15

Now you can see that you just add the exponents and multiply the constants.

Answer 16

So that would be 49ab6 right

Answer 17

\[ (5x^4y^2z^2)(3x^4y^3z^5)\]

\[ (5x^4*3x^4*y^2*y^3*z^5*z^2)\]

\[5*3*x ^{4+4}*y ^{2+3}*z ^{5+2}\]

\[15x^8y^5z^7\]

Answer 18

Thank you @Nurali

Answer 19

Yeah, that's right.

Answer 20

Yay!

Answer 21

Anytime.

Answer 22

Sorry, no, it's\[49a^2b^6\]

Answer 23

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

4x7y10

4x9y10

4x14y16

4x14y17

Answer 24

You forgot to add the powers on the a.

Answer 25

OOPS.

Answer 26

Ohhhh I see now

Answer 27

Lol

Answer 28

Okay. This next one is just like the last one, except it's a problem in a problem. Let's take it step by step.

Answer 29

Ok

Answer 30

First, do the power to a powers. \[(2x7y)^2 * (y^5)^3 = (2x7y)(2x7y)*(y^5)(y^5)(y^5)\]

Answer 31

Can you simplify that?

Answer 32

a little confused

Answer 33

First do the 2x7y part. There's an imaginary exponent of 1 on top of each of them. What's 1+1?

Answer 34

(wow, I feel stupid)

Answer 35

lolllll

Answer 36

2

Answer 37

Oh, wait. Is that\[2x7y\]or \[2x^7y\]

Answer 38

Because there's a significant difference.

Answer 39

Second option

Answer 40

OK. Nevermind, then!

Answer 41

It's time to learn a shortcut.

Answer 42

The one where the 7 is higher

Answer 43

Lol Im ready

Answer 44

Any time you have a problem of the form\[((some constant)*a^x*b^y)^c\]

Answer 45

You multiply x and c as well as y and c, but take the constant to the c power. So it's\[(someconstant)^c*a ^{xc}*b^{yc}\]

Answer 46

In this case, we have \[(2x^7y)^2\]

Answer 47

Hmm? What would be the constant

Answer 48

Oh

Answer 49

Can you evaluate that? Just multiply the 2 by the exponents and take 2^2.

Answer 50

And remember it's technically y^1.

Answer 51

Ok so that would be 2

Answer 52

Sorry im a little bit slow with math :c

Answer 53

oh wait wouldnt that be 14 and 4 @oaktree

Answer 54

Like \[4x^{14}y^2\]

Answer 55

Ohh ok that makes a lot more sense

Answer 56

:-)

Answer 57

My question is a little different then this one

Answer 58

Thank You @Oaktree