Final answer:
To solve the equation 1/16 = 64⁴ˣ⁻³, we can rewrite 64 as a power of 2 and simplify the exponents. However, this leads to an equation that has no solution.
Step-by-step explanation:
To solve the equation 1/16 = 64⁴ˣ⁻³, we need to apply the properties of exponents. First, let's rewrite 64 as a power of 2: 64 = 2⁶. Now, we can substitute this into the equation:
1/16 = (2⁶)⁴ˣ⁻³
To simplify the equation further, we can simplify the exponents. Cubing the exponent 4 gives us 4³ = 64, and multiplying the exponent 6 by 3 gives us 3(6) = 18. Applying these simplifications:
1/16 = 2⁶ˣ⁻³ = (2³)¹⁸⁻³ = 2⁶
Now, we have a simpler equation that we can solve. Taking the square root of both sides:
√(1/16) = √(2⁶)
1/4 = 2³
Finally, we have the equation 1/4 = 8. This means that the original equation has no solution.