Question

PLEASE HELP!! write as a single power of 4: √64 * (4√128)^3

Answer 1

so : you need some knowledge about exponential laws. You can find that in your text book.

anyhow. \[4^{3} = 64 \Leftrightarrow \sqrt{64} = \sqrt{4^{3}}, \text{you probably know this}\] so we also know that \[4*4*4*2 = 128 \Leftrightarrow \sqrt{128}= \sqrt{4*4*4*2}\]

Answer 2

Is the 4 before radical 128 the fourth root or just 4 * sqrt(128) ?

Answer 3

A = 4^x, where you calculate A from your square roots etc.

log A = x log (4) so x = log A / log 4

Unfortunately, I got a large A and x=10.75, but you may calculate better than I.

Answer 4

fourth root.
Also, it has to be a single power.
i.e. \[\sqrt[3]{16}\] = 16 ^ 1/3 = 4^2/3

Answer 5

\[\Large \sqrt{64} * (\sqrt[4]{128})^3 = (64)^{1/2} * (128)^{3/4}\]

Answer 6

simplify.

Answer 7

\[64 = 2 * 2 * 2 * 2 * 2 * 2 = 2^6 ; \quad 128 = 64 * 2 = 2^7\]

Answer 8

\[(64)^{1/2} * (128)^{3/4} = ((2)^6)^{1/2} * ((2^7))^{3/4} = 2^3 * 2^{21/4} = 2^{3+21/4} = 2^{33/4}\]

Answer 9

We want a single power of 4. The base 2 can be written as square root of 4:\[\Large 2^{33/4} = (\sqrt{4})^{33/4} = (4^{1/2})^{33/4} = 4^{33/8}\]

Answer 10

Thanks!

Answer 11

you are welcome.