Question

Can anyone help me solve this? I will give medal to whoever helps!

3 Sqrt. (2^6)^x

Answer 1

\[4^{x}\]
this is because exponents of exponents are the same when multiplied. i.e.
\[2^{6^{x}} = 2^{6x}\]
and roots become exponent division so
\[\sqrt[3]{2^{6^{x}}} = 2^{2^{x}} = 4^{x}\]

Answer 2

\[\sqrt[3]{\left( 2^{6} \right)}^{x}\]

Answer 3

okay! thanks! could you explain that second part in a little more detail? The first part makes sense... but what do you do with the 3?

Answer 4

so after you change it to \[\sqrt[3]{2^{6x}}\] what do you do?

Answer 5

sure, happy to help!
Every root is actually an exponent of a fractional amount.
\[\sqrt[2]{x} = x ^{\frac{ 1 }{ 2 }}\]
so \[\sqrt[3]{2^{6^{x}}} = (2^{6\times \frac{ 1 }{ 3 }})^{x} = 2^{2^{x}}\]

Answer 6

oh, okay!! thank you soooo much!! :))

Answer 7

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