Find the positive solution of the equation. 8x^((5)/(8))+27=283 Answer:

Isolate Variable Term: Isolate the term with the variable. Subtract 27 from both sides of the equation to isolate the term with the variable x. 8x^(5/8) + 27 - 27 = 283 - 27 8x^(5/8) = 256Subtract 27: Divide both sides by 8 to solve for x^(5/8). 8x^(5/8) / 8 = 256 / 8 x^(5/8) = 32Divide by 8: Recognize that 32 is a power of 2. 32 can be written as 2^5 because 2^5 = 32. x^(5/8) = 2^5Recognize Power of 2: Raise both sides of the equation to the reciprocal of the exponent on x to solve for x. (x^(5/8))^(8/5) = (2^5)^(8/5) x = 2^(5 * 8/5) x = 2^8Raise to Reciprocal Exponent: Calculate 2^8 to find the value of x. 2^8 = 256 x = 256

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Find the positive solution of the equation.

8x^((5)/(8))+27=283
Answer:

Find the positive solution of the equation. $\newline$ $8 x^{\frac{5}{8}}+27=283$ $\newline$ Answer:

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Q. Find the positive solution of the equation.

\newline

8 x^{\frac{5}{8}}+27=283

\newline

Answer:

Isolate Variable Term: Isolate the term with the variable. $\newline$ Subtract $27$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $8x^{(5/8)} + 27 - 27 = 283 - 27$ $\newline$ $8x^{(5/8)} = 256$
Subtract $27$ : Divide both sides by $8$ to solve for $x^{\frac{5}{8}}$ . $\newline$ $\frac{8x^{\frac{5}{8}}}{8} = \frac{256}{8}$ $\newline$ $x^{\frac{5}{8}} = 32$
Divide by $8$ : Recognize that $32$ is a power of $2$ . $32$ can be written as $2^5$ because $2^5 = 32$ . $x^{\frac{5}{8}} = 2^5$
Recognize Power of $2$ : Raise both sides of the equation to the reciprocal of the exponent on $x$ to solve for $x$ . $(x^{5/8})^{8/5} = (2^5)^{8/5}$ $x = 2^{5 \cdot 8/5}$ $x = 2^8$
Raise to Reciprocal Exponent: Calculate $2^8$ to find the value of $x$ . $\newline$ $2^8 = 256$ $\newline$ $x = 256$