Solve for x:

\[ x^{-3} = \frac{27}{64} \]

Remember what a negative exponent means ... it's just a positive exponent in the denominator of a fraction. 'x' to negative 3rd power is the same as 1/x³ .
1/x³ = 27/64
Take the reciprocal of each side:
x³ = 64/27
x= ∛64/27 = ∛64 / ∛27.
64 is the perfect cube of 4. 27 is the perfect cube of 3.
x = 4/3 .

Answered by AL2006 | 2024-06-10

To solve x − 3 = 64 27 ​ , we rewrite it as x 3 1 ​ = 64 27 ​ and take the reciprocal to get x 3 = 27 64 ​ . Taking the cube root gives x = 3 4 ​ .
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Answered by AL2006 | 2024-10-31