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

15x16y6z10
15x8y5z7
8x8y5z7
8x16y6z

Question

Choose the correct simplification of the expression (5x4y2z2)(3x4y3z5).
 	
	15x16y6z10
	15x8y5z7
	8x8y5z7
	8x16y6z

johnweldon1993 · Answer

Lets see what we got here :P

$$\large (5x^4 y^2 z^2)(3x^4 y^3 z^5)$$

right?

anonymous · Answer

yess sirr. c:

johnweldon1993 · Answer

Alright...so all we need to do is multiply the terms together

we can eliminate 2 options off the bat because we know 5 times 3 = 15 right

so C and D are gone...

johnweldon1993 · Answer

Nowwww, when we multiply exponents with the same base

example x^4 and x^4 here...what do we do? or what do we get?

anonymous · Answer

16?

anonymous · Answer

is that what we get or no?

johnweldon1993 · Answer

Not quite, the rules of exponents actually say that

$$\large x^4\times x^4 = x^{4 + 4}$$

johnweldon1993 · Answer

We only multiply the exponents if we have something like

$\large (x^4)^4$ when they are directly separated by a parenthesis...then we multiply

but otherwise *and here* we add the exponents...

so $$\large x^4 \times x^4 = x^{4 + 4} =x^8$$

anonymous · Answer

oh.

johnweldon1993 · Answer

And we can keep going *theres only 1 answer choice with x^8 on here but for practice lol*

$$\large y^2 \times y^3 = ?$$

and

$$\large z^2 \times z^5 = ?$$

anonymous · Answer

y=6 ?

anonymous · Answer

idk this all confuses me

johnweldon1993 · Answer

Not quite...we need to add the exponents

So imagine we are doing something easier like

$$\large (2^6)(2^3)$$

and we want to know what that is...now we see that the base number (2) is the same in both cases...so we are going to leave it alone...and we are going to just add the exponents 

so

$$\large (2^6)(2^3) \rightarrow 2^{6 + 3} \rightarrow 2^9$$

and it works the same here

johnweldon1993 · Answer

So here...we just focus on say the 'y' terms

we have

$$\large (y^2)(y^3)$$

this time...the base number *which is 'y'* is the same in both cases...so we leave it alone...and just add the exponents

$$\large (y^2)(y^3) \rightarrow y^{2 + 3} \rightarrow y^5$$

johnweldon1993 · Answer

Is that making a little more sense maybe?

anonymous · Answer

okay. yeah i get it little bit more now.

johnweldon1993 · Answer

Okay, so test time :P

If we have

$$\large (z^2)(z^5)$$

what would that be?

anonymous · Answer

$$z ^{7}$$

johnweldon1993 · Answer

Perfect :)

Alright good...

so now it is confirmed that our simplification was

$$\large 15x^8y^5z^7$$

anonymous · Answer

thank you.

johnweldon1993 · Answer

Anytime! If you need any more clarification just tag me back or message me :)