Answer:
x=1
Step-by-step explanation:
The equation can be simplified and solved using the rules of exponents and the usual inverse operations.
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Interpreted according to the Order of Operations, your equation is ...
((2^2)x)^3 = 64
(4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)
x^3 = 1 . . . . . . . . . . . . . . divide by 64
x = ∛1 = 1
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Perhaps you want x in the exponent:
(2^(2x))^3 = 64
2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)
6x = 6 . . . . . . . . match exponents
x = 1 . . . . . . divide by 6
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Additional comment
Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.
