IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng eksaktong sagot. Magtanong ng anumang bagay at makatanggap ng kumpleto at eksaktong sagot mula sa aming komunidad ng mga propesyonal.
The expression
[tex]{x}^{7} - 128[/tex]
is factorable by the factor theorem: since x = 2 is a root (a number which yields 0 when substituted), x - 2 is a factor.
However, dividing x⁷ - 128 by x - 2 gives a quotient which is a sixth-degree polynomial. So, the easiest way to solve for x is by setting x⁷ - 128 equal to 0.
[tex] {x}^{7} - 128 = 0[/tex]
First, we isolate the variable by adding 128 to both sides:
[tex] {x}^{7} = 128[/tex]
Notice that 128 is a power of 2. Precisely, the seventh power of 2. So, we may rewrite 128 as 2⁷.
[tex] {x}^{7} = {2}^{7} [/tex]
By laws of exponents, since the powers are equal, the bases must be equal.
Therefore, x = 2.