Compare and Contrast: Below are two expressions. Simplify each and then choose the statement that is true. (1 point) Expression #1 Expression #2 (3x2)3x2 (3x3)2(x2) The exponents in Expression #1 are greater than the exponents of Expression #2. The exponents on Expression #2 are greater than the exponents of Expression #1. The exponents of Expression #1 are the same as the exponents of Expression #2. The relationship cannot be determined with the given information.
\[(3x^2)3x^2\]
\[(3x^3)^2(x^2)\]
@zepdrix
can you please help.???
have kno understanding what it means
have no understanding what it means
I don't know what they mean by "exponents", plural... that's making the problem extra confusing. They want us to simplify, then compare the power of the 3 AND the x? Let's check out expression 1,\[\large\rm (3x^2)3x^2\quad=\quad 3\cdot3\cdot x^2\cdot x^2\]Whenever we multiply things of the same base, we add the exponents,\[\large\rm =3^2\cdot x^{2+2}\]
So for expression 1 we have \(\large\rm 3^2x^4\)
right...
In expression 2,\[\large\rm (3x^3)^2(x^2)\]When you have an exponent being applied to a group, you have to give the exponent to each thing in that group,\[\large\rm =3^2(x^3)^2(x^2)\]So I gave the square to the 3 and to the x^3. Next, when we have a power and another power being applied, our exponent rule tells us to multiply the powers. So (x^3)^2 will be become x^(3*2) which is x^6.\[\large\rm =3^2\cdot x^6(x^2)\]And again we apply the addition rule from before, same base multiplying, so we ADD the exponents,\[\large\rm 3^2\cdot x^{6+2}\]
So our second expression is giving us,\[\large\rm 3^2x^8\]
So it turns out that none of these options are correct. One of the exponents is the same, while another is larger than the other. Maybe typo in the question... doesn't make sense :(
hmm
I'll do screen shot
@zepdrix
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you know who can help me Qwertty123?
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expression 1: \[(3x^2)3x^2= 3*3*x^2*x^2=9x^4\]right?
Mhm ^.^
yes, i think
expression 2: \[(3x^3)^23x^2= (3x^3*3x^3)3x^2\] can you simplify that the rest of the way?
ok, i'll try...
remember, when you multiply exponentials, if the base is the same, you add the exponents. \[x^3*x^4=x^{3+4}=x^7\]
1. \[27x^6\]
sorry it glitched up
so it's B. right?
yes, very good!
thank you what a relief.
sorry, B is correct answer, but your simplification is incorrect. \[(3x^3)^2(x^2)=(3x^3*3x^3)*x^2 = 9x^6*x^2=9x^8\]
oh, I see my problem my bet :)
another way of doing it would be\[(3x^3)^2*x^2=3^2*(x^3)^2*x^2=9*x^6*x^2=9x^8\]
ok
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