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Mathematics
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OpenStudy (anonymous):
Simplify the expression
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OpenStudy (anonymous):
\[\sqrt[4]{16a^6b ^{12}}\]
OpenStudy (solomonzelman):
\(\Large\color{red}{ \bf \sqrt[4]{16a^{16}b^{12}} }\)
\(\Large\color{red}{ \bf \sqrt[4]{(2a^4)^{4}~~(b^{3})^4} }\)
OpenStudy (shamim):
16=2^4
OpenStudy (solomonzelman):
can you finish the problem ?
OpenStudy (anonymous):
\[2a^4b^3\]
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OpenStudy (solomonzelman):
yes, correct !
OpenStudy (anonymous):
no First express the radical in exponential form. Treat each factor separately.
OpenStudy (anonymous):
\[b ^{\frac{ m }{ n }} = \sqrt[n]{b ^{m}} = \left( \sqrt[n]{b} \right)^m\]
OpenStudy (solomonzelman):
\(\large\color{blue}{ \rm (2^3)^4 =16}\)
\(\large\color{blue}{ \rm (a^4)^4 =a^{16} }\)
\(\large\color{blue}{ \rm (b^3)^4 =b^{12} }\)
OpenStudy (anonymous):
here is the answer
\[2ab^3\sqrt{a}\]
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OpenStudy (anonymous):
but you get an A for effort so heres your medal...
OpenStudy (solomonzelman):
Yes I meant 2^4=16... not (2^3)^4 =16
OpenStudy (solomonzelman):
I don't really think that I am wrong. I know this stuff fairly well ;)
You are leaving some exponents out.
OpenStudy (anonymous):
No that was the exact question posted directly from the sheet its self
nothing was left out
OpenStudy (solomonzelman):
then what I said is correct.
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