Find the positive solution of the equation. 4x^((7)/(9))+28=65564 Answer:

Isolate variable x: Subtract 28 from both sides of the equation to isolate the term with the variable x. 4x^(7/9) + 28 - 28 = 65564 - 28 4x^(7/9) = 65536Solve for x^(7/9): Divide both sides of the equation by 4 to solve for x^(7/9). (4x^(7/9)) / 4 = 65536 / 4 x^(7/9) = 16384Recognize power of 2: Recognize that 16384 is a power of 2. Specifically, 16384 = 2^14. x^(7/9) = 2^14Raise to reciprocal exponent: Raise both sides of the equation to the reciprocal of (7/9) to solve for x. (x^(7/9))^(9/7) = (2^14)^(9/7) x = 2^(14 * 9/7)Simplify exponent: Simplify the exponent on the right side of the equation. x = 2^(18)Calculate final value: Calculate 2^18 to find the value of x. x = 262144

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Q. Find the positive solution of the equation.

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4 x^{\frac{7}{9}}+28=65564

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Answer:

Isolate variable x: Subtract $28$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $4x^{(7/9)} + 28 - 28 = 65564 - 28$ $\newline$ $4x^{(7/9)} = 65536$
Solve for $x^{\frac{7}{9}}$ : Divide both sides of the equation by $4$ to solve for $x^{\frac{7}{9}}$ . $\frac{4x^{\frac{7}{9}}}{4} = \frac{65536}{4}$ $x^{\frac{7}{9}} = 16384$
Recognize power of $2$ : Recognize that $16384$ is a power of $2$ . Specifically, $16384 = 2^{14}$ . $x^{\frac{7}{9}} = 2^{14}$
Raise to reciprocal exponent: Raise both sides of the equation to the reciprocal of $\frac{7}{9}$ to solve for $x$ . $\left(x^{\frac{7}{9}}\right)^{\frac{9}{7}} = \left(2^{14}\right)^{\frac{9}{7}}$ $x = 2^{14 \cdot \frac{9}{7}}$
Simplify exponent: Simplify the exponent on the right side of the equation. $x = 2^{18}$
Calculate final value: Calculate $2^{18}$ to find the value of $x$ . $\newline$ $x = 262144$