Question

solución de ecuaciones exponenciales de varios paso resolver: \\(\frac{512^{x - 2}}{\left(\frac{1}{64}\
ight)^{3x}} = 512\\) \\(x = 1\\) no hay solución \\(x = 0\\) \\(x = -1\\)

Explanation:

Step1: Express bases as powers of 2

512 is \(2^9\), \(\frac{1}{64}\) is \(2^{-6}\). So rewrite the equation:
\(\frac{(2^9)^{x - 2}}{(2^{-6})^{3x}} = 2^9\)

Step2: Simplify exponents

Using \((a^m)^n = a^{mn}\), we get:
\(\frac{2^{9(x - 2)}}{2^{-18x}} = 2^9\)

Step3: Use exponent division rule

\(a^m \div a^n = a^{m - n}\), so:
\(2^{9(x - 2) - (-18x)} = 2^9\)

Step4: Simplify the exponent

Expand and combine like terms:
\(9x - 18 + 18x = 9\)
\(27x - 18 = 9\)

Step5: Solve for x

Add 18 to both sides: \(27x = 27\)
Divide by 27: \(x = 1\)

Answer:

x = 1 (corresponding to the option "x = 1")