Question

(1/8) raised to -x ppwer= 64 raised to x powerI'll upload a picture

Answer 1

x = 0

Step-by-step explanation:
`((1)/(8))^(-x)=64^x`
`\begin{gathered} \frac{1}{8\text{ }}\text{ = }(1)/(2^3)\text{ } \\ \text{Rule: }(1)/(a^b)=a^(-b) \\ so,\text{ }(1)/(2^3)=2^(-3) \\ (\frac{1}{8\text{ }})^(-x)=((1)/(2^3))^(-x)\text{ = }(2^(-3))^(-x) \\ =2^(3x) \end{gathered}`
`\begin{gathered} 64=2^6 \\ 64^x=(2^6)^x=2^(6x) \\ ((1)/(8))^(-x)=64^x \\ 2^(3x)\text{ = }2^(6x) \\ \text{base cancels out:} \\ 3x\text{ = 6x} \end{gathered}`
`\begin{gathered} 3x\text{ - }6x\text{ = 0 } \\ -3x\text{ = 0} \\ \text{divide both sides by -3:} \\ (-3x)/(-3)\text{ = }(0)/(-3) \\ x\text{ = 0} \end{gathered}`