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Mathematics 19 Online
OpenStudy (anonymous):

3radical 64a^16

OpenStudy (solomonzelman):

\[\huge\color{blue}{ \sqrt[3]{64a^{16}} }~~~~~~~~~~~~~~~~~~~~this?\]

OpenStudy (anonymous):

yes

OpenStudy (solomonzelman):

you can re-write it as.\[\huge\color{blue}{ \sqrt[3]{4^3a^{15}\times a} }\]

OpenStudy (kc_kennylau):

\[\huge\sqrt[3]{64a^{16}}=\sqrt[3]{64}\sqrt[3]{a^{16}}=\sqrt[3]{4\times4\times4}\sqrt[3]{a^5\times a^5\times a^5\times a}\]

OpenStudy (kc_kennylau):

Sorry the a is hidden on the right

OpenStudy (anonymous):

i have to see what its equivalent to

OpenStudy (solomonzelman):

\[\huge\color{orangered}{ \sqrt[3]{64a^{16}} }=\huge\color{orangered}{ \sqrt[3]{4^3a^{15} \times a }}\]\[\huge\color{orangered}{ =\sqrt[3]{4^3~~(a^5){3}~~\times a} }\]

OpenStudy (solomonzelman):

Can you simplify that?

OpenStudy (solomonzelman):

the last thing is supposed to be \[\huge\color{lime}{ \sqrt[3]{4^3~(a^5)~^{3} \times a} }\]

OpenStudy (kc_kennylau):

\[\huge\begin{array}{}&\sqrt[3]{64a^{16}}\\=&\sqrt[3]{64}\times\sqrt[3]{a^{16}}\\=&\sqrt[3]{4\times4\times4}\times\sqrt[3]{a^5\times a^5\times a^5\times a}\\=&4\times a^5\sqrt[3]a\end{array}\]

OpenStudy (anonymous):

thank you so much!

OpenStudy (kc_kennylau):

Do you understand the WHOLE concept now?

OpenStudy (anonymous):

yes

OpenStudy (kc_kennylau):

That means if I were to give you one more question of the same type, would you be able to solve it?

OpenStudy (kc_kennylau):

(Don't worry, I won't)

OpenStudy (anonymous):

yes I know what it means

OpenStudy (kc_kennylau):

Glad to know, just to get me out of trouble.

OpenStudy (anonymous):

lol ty merry christmas

OpenStudy (kc_kennylau):

thx u2 :D

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