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You can simplify the right side. Then, you need to take cube roots.
(m -4)³ = 1/(1/8) . . . rule of exponents
(m -4)³ = 8 . . . . . . .simplify
m -4 = ∛8 . . . . . . . take cube roots
m -4 = 2 . . . . . . . . use your calculator or knowledge to find ∛8
m = 6 . . . . . . . . . . add 4
The solution is m = 6.
_____
If you subtract the right side, you get a function of m that is zero when m has the right value. This graph shows that value is m = 6.
(m -4)³ = 1/(1/8) . . . rule of exponents
(m -4)³ = 8 . . . . . . .simplify
m -4 = ∛8 . . . . . . . take cube roots
m -4 = 2 . . . . . . . . use your calculator or knowledge to find ∛8
m = 6 . . . . . . . . . . add 4
The solution is m = 6.
_____
If you subtract the right side, you get a function of m that is zero when m has the right value. This graph shows that value is m = 6.