+997 If \((4-a)^3 = 32\), then what is \(a\)?
Answer is \(a = 4-2\sqrt[3]{4}\).
I just need work finding the solution.
+9466 \((4-a)^3\ =\ 32\)
Take the cube root of both sides of the equation.
\(\sqrt[3]{(4-a)^3}\ =\ \sqrt[3]{32}\)
Simplify the left side with the rule \(\sqrt[3]{n^3}\ =\ n\)
\(4-a\ =\ \sqrt[3]{32}\)
We can rewrite 32 like this because 32 = 2 * 2 * 2 * 2 * 2
\(4-a\ =\ \sqrt[3]{2\cdot2\cdot2\cdot2\cdot2}\)
We can rewrite the right side again like this...
\(4-a\ =\ \sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{2\cdot2}\)
And 2 * 2 * 2 = 23 and 2 * 2 = 4
\(4-a\ =\ \sqrt[3]{2^3}\,\cdot\,\sqrt[3]{4}\)
Simplify \(\sqrt[3]{2^3}\) again with the rule \(\sqrt[3]{n^3}\ =\ n\)
\(4-a\ =\ 2\,\cdot\,\sqrt[3]{4}\)
\(4-a\ =\ 2\sqrt[3]{4}\)
Add a to both sides of the equation.
\(4\ =\ 2\sqrt[3]{4}+a\)
Subtract \(2\sqrt[3]{4}\) from both sides of the equation.
\(4-2\sqrt[3]{4}\ =\ a\)
\(a\ =\ 4-2\sqrt[3]{4}\)-
+36916 (4-a)^3 = 32 cube root both sides (note that 32 = 2^5 )
(4-a) = cubrt(2^5) Simplify the right side
(4-a) = 2 cubrt(4) Add 'a' to both sides and subtract 2 cubrt(4) from both sides
4- 2 cubrt(4) = a
