Find the positive solution of the equation. 6x^((8)/(5))-28=100663268 Answer:

Add 28 to isolate variable: Add 28 to both sides of the equation to isolate the term with the variable. \[6x^{\frac{8}{5}} - 28 + 28 = 100663268 + 28\] \[6x^{\frac{8}{5}} = 100663296\]Divide by 6: Divide both sides of the equation by 6 to solve for $x^{\frac{8}{5}}$. \[\frac{6x^{\frac{8}{5}}}{6} = \frac{100663296}{6}\] \[x^{\frac{8}{5}} = 16777216\]Recognize power of 2: Recognize that $16777216$ is a power of 2. Specifically, $16777216 = 2^{24}$.Replace with 2^24: Write the equation with $2^{24}$ in place of $16777216$. \[x^{\frac{8}{5}} = 2^{24}\]Raise to power of 5/8: Raise both sides of the equation to the power of $\frac{5}{8}$ to solve for $x$. \[\left(x^{\frac{8}{5}}\right)^{\frac{5}{8}} = \left(2^{24}\right)^{\frac{5}{8}}\] \[x = 2^{24 \cdot \frac{5}{8}}\] \[x = 2^{15}\]Calculate 2^15: Calculate the value of $2^{15}$. \[2^{15} = 32768\]

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Q. Find the positive solution of the equation.

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6 x^{\frac{8}{5}}-28=100663268

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Answer:

Add $28$ to isolate variable: Add $28$ to both sides of the equation to isolate the term with the variable. $\newline$ $6x^{\frac{8}{5}} - 28 + 28 = 100663268 + 28$ $\newline$ $6x^{\frac{8}{5}} = 100663296$
Divide by $6$ : Divide both sides of the equation by $6$ to solve for $x^{\frac{8}{5}}$ . $\newline$ $\frac{6x^{\frac{8}{5}}}{6} = \frac{100663296}{6}$ $\newline$ $x^{\frac{8}{5}} = 16777216$
Recognize power of $2$ : Recognize that $16777216$ is a power of $2$ . Specifically, $16777216 = 2^{24}$ .
Replace with $2$ ^ $24$ : Write the equation with $2^{24}$ in place of $16777216$ . $\newline$ $x^{\frac{8}{5}} = 2^{24}$
Raise to power of $5$ / $8$ : Raise both sides of the equation to the power of $\frac{5}{8}$ to solve for $x$ . $\newline$ $\left(x^{\frac{8}{5}}\right)^{\frac{5}{8}} = \left(2^{24}\right)^{\frac{5}{8}}$ $\newline$ $x = 2^{24 \cdot \frac{5}{8}}$ $\newline$ $x = 2^{15}$
Calculate $2$ ^ $15$ : Calculate the value of $2^{15}$ . $\newline$ $2^{15} = 32768$