They usually don't give complicated problems until after you have studied easy problems.
so you should have learned this rule:
\[ \left( a^b\right)^c = a^{bc} \]
in other words, you can multiply the exponents b*c
example:
\[ \left( 2^3\right)^4 = 2^{3 \cdot 4} = 2^{12}\]
can you use that rule to rewrite
\[ \left( 2^3\right)^x \]?
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OpenStudy (horsegirl27):
ok
OpenStudy (horsegirl27):
2^3x
OpenStudy (horsegirl27):
right?
OpenStudy (phi):
yes. now for your problem
\[ \left(2^6 \right)^x= 2^{6x} \]
OpenStudy (horsegirl27):
ok
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OpenStudy (phi):
now use the rule
\[ \sqrt[a]{b} = \left( b \right)^\frac{1}{a} \]
the little "a" next to the root sign is turned into the fraction 1/a and made an exponent
for our problem, b is "complicated" = \( 2^{6x} \)
but that does not matter. write:
\[ \sqrt[3]{2^{6x}} = \left(2^{6x} \right)^\frac{1}{3} \]
OpenStudy (phi):
now use the first rule again: multiply the 6x times the 1/3
to get a new exponent.
can you do that ?
OpenStudy (horsegirl27):
yes
OpenStudy (horsegirl27):
2^3x?
OpenStudy (phi):
the x part is ok. but what is 6 * 1/3 ?
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OpenStudy (horsegirl27):
oops 2!
OpenStudy (phi):
yes, so
\[ 2^{2x} \]
now we use the first rule, but "backwards"
the exponent is 2 times x, so we can "undo" that and write it as
\[ \left(2^2\right)^x \]
does that make sense?
OpenStudy (horsegirl27):
Sort of.
OpenStudy (horsegirl27):
Actually it does
OpenStudy (phi):
notice we could also write
\[ 2^{2x} = \left(2^x\right)^2 \]
but for this problem we want to write it as
\[ 2^{2x} = \left(2^2\right)^x \]
do you have any idea what 2^2 is ? (what number?)
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OpenStudy (horsegirl27):
4
OpenStudy (phi):
yes, which means
\[ \left(2^2\right)^x = (4)^x = 4^x \]
OpenStudy (horsegirl27):
ok
OpenStudy (horsegirl27):
that would mean Anna is correct
OpenStudy (phi):
so anna did it correctly
blake did something goofy
christine wrote the little "root 3" as exponent 3 instead of 1/3
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OpenStudy (horsegirl27):
ok
OpenStudy (horsegirl27):
Now what about number 2 @phi
OpenStudy (horsegirl27):
@iGreen help!
OpenStudy (horsegirl27):
@Sweeni
OpenStudy (horsegirl27):
@triciaal @satellite73 @iGreen @Nnesha help me!!!
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OpenStudy (horsegirl27):
@ribhu please help
OpenStudy (ribhu):
which question?
OpenStudy (horsegirl27):
2-4
OpenStudy (anonymous):
Maybe you should do your own homework. Since everyone on here is giving out direct answers without explanations, so the asker won't learn anything. My advice is, you should do it yourself. I went through the messages on this post and you seem very smart, you have the answer for every question. You seem as though you know what you're doing, so why not give it a go? My advice is, you should do them by yourself, so you can at least learn something. These aren't difficult questions either, good luck.
OpenStudy (horsegirl27):
Ok. I just doubt myself and like someone there to help me when I feel I need it. And I am learning. and I do need help getting started I'm not sure what to do as my first step
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OpenStudy (ribhu):
OpenStudy (anonymous):
Um hi
OpenStudy (ribhu):
@horsegirl27 u there i have solved 3 & 4 also but not able to post them
OpenStudy (ribhu):
OpenStudy (anonymous):
me
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OpenStudy (anonymous):
?
OpenStudy (ribhu):
OpenStudy (ribhu):
solutions to 2,3&4
OpenStudy (ribhu):
@Supermariofan153 i hope solutions are legible
OpenStudy (horsegirl27):
You have good handwriting I can read the first page I will look at the others
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OpenStudy (horsegirl27):
so for 4, basically he's correct that if the length is irrational, the area and perimeter are always irratioal?
OpenStudy (horsegirl27):
*irrational
OpenStudy (ribhu):
yeah
OpenStudy (horsegirl27):
And 3 is a little hard to read... But could you briefly explain it? at least the key points then I will be able to figure out what you wrote
OpenStudy (horsegirl27):
ok
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