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Solve the exponential equation for 
x.

{:[4^(9-6x)=((1)/(64))^((10)/(3))],[x=◻]:}

Solve the exponential equation for x x .\newline496x=(164)103x= \begin{array}{l} 4^{9-6 x}=\left(\frac{1}{64}\right)^{\frac{10}{3}} \\ x=\square \end{array}

Full solution

Q. Solve the exponential equation for x x .\newline496x=(164)103x= \begin{array}{l} 4^{9-6 x}=\left(\frac{1}{64}\right)^{\frac{10}{3}} \\ x=\square \end{array}
  1. Write Equation: Write down the given exponential equation.\newline496x=(164)1034^{9-6x} = \left(\frac{1}{64}\right)^{\frac{10}{3}}
  2. Use Power Property: Recognize that 164\frac{1}{64} can be written as 434^{-3} because 6464 is 434^3. \newline496x=(43)1034^{9-6x} = (4^{-3})^{\frac{10}{3}}
  3. Simplify Right Side: Simplify the right side of the equation using the power of a power property amn=(am)na^{m*n} = (a^m)^n.\newline496x=4104^{9-6x} = 4^{-10}
  4. Set Exponents Equal: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. 96x=109 - 6x = -10
  5. Isolate Variable: Solve for xx by isolating the variable.\newlineAdd 6x6x to both sides:\newline9=6x109 = 6x - 10
  6. Add 1010: Add 1010 to both sides to isolate the term with xx.\newline19=6x19 = 6x
  7. Divide by 66: Divide both sides by 66 to solve for xx.x=196x = \frac{19}{6}

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