Question

Multiply and simplify by factoring

fourth root 16 * fourth root 128

Answer 1

\[16=2^4\] so
\[\sqrt[4]{16}=2\] is a start

Answer 2

yea I got that 2 lol but the second part threw me off

Answer 3

\[128=2^7\] so
\[\sqrt[4]{128}=2\sqrt[4]{2^3}\]

Answer 4

this is how i did it in my head.
the exponent is 7, the "index" is 4
4 goes in to 7 one time so a 2 comes out
the remainder is 3, so a 2^3 stays in

Answer 5

yea that makes sense

Answer 6

that explains this line
\[\sqrt[4]{128}=\sqrt[4]{2^7}=2\sqrt[4]{2^3}=2\sqrt[4]{8}\]

Answer 7

so your 'final answer' is
\[2\times 2\sqrt[4]{8}=4\sqrt[4]{8}\]