Find the positive solution of the equation. 8x^((3)/(4))+16=232 Answer:

Isolate variable term: Isolate the term with the variable. Subtract 16 from both sides of the equation to isolate the term with the variable x. 8x^(3/4) + 16 - 16 = 232 - 16 8x^(3/4) = 216Divide by 8: Divide both sides by 8 to solve for x^(3/4). 8x^(3/4) / 8 = 216 / 8 x^(3/4) = 27Recognize perfect cube: Recognize that 27 is a perfect cube and can be written as 3^3. Since we have x^(3/4) = 27 and 27 = 3^3, we can write: x^(3/4) = 3^3Raise to power: Raise both sides of the equation to the power of 4/3 to solve for x. (x^(3/4))^(4/3) = (3^3)^(4/3) Using the property of exponents (a^(m/n))^p = a^(m*p/n), we get: x = 3^(3*4/3) x = 3^4Calculate final value: Calculate 3^4 to find the value of x. 3^4 = 3 * 3 * 3 * 3 3^4 = 81 Therefore, x = 81

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Q. Find the positive solution of the equation.

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8 x^{\frac{3}{4}}+16=232

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Answer:

Isolate variable term: Isolate the term with the variable. $\newline$ Subtract $16$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $8x^{(3/4)} + 16 - 16 = 232 - 16$ $\newline$ $8x^{(3/4)} = 216$
Divide by $8$ : Divide both sides by $8$ to solve for $x^{\frac{3}{4}}$ . $\newline$ $\frac{8x^{\frac{3}{4}}}{8} = \frac{216}{8}$ $\newline$ $x^{\frac{3}{4}} = 27$
Recognize perfect cube: Recognize that $27$ is a perfect cube and can be written as $3^3$ . Since we have $x^{\frac{3}{4}} = 27$ and $27 = 3^3$ , we can write: $x^{\frac{3}{4}} = 3^3$
Raise to power: Raise both sides of the equation to the power of $\frac{4}{3}$ to solve for $x$ .
$(x^{\frac{3}{4}})^{\frac{4}{3}} = (3^3)^{\frac{4}{3}}$
Using the property of exponents $(a^{\frac{m}{n}})^p = a^{\frac{m*p}{n}}$ , we get:
$x = 3^{\frac{3*4}{3}}$
$x = 3^4$
Calculate final value: Calculate $3^4$ to find the value of $x$ . $\newline$ $3^4 = 3 \times 3 \times 3 \times 3$ $\newline$ $3^4 = 81$ $\newline$ Therefore, $x = 81$