Question

question
find the positive solution of the equation.
$3x^{\frac{9}{4}} - 25 = 121060796$

Explanation:

Step1: Isolate the variable term

Add 25 to both sides.
$$3x^{\frac{9}{4}} = 121060796 + 25$$
$$3x^{\frac{9}{4}} = 121060821$$

Step2: Solve for $x^{\frac{9}{4}}$

Divide both sides by 3.
$$x^{\frac{9}{4}} = \frac{121060821}{3}$$
$$x^{\frac{9}{4}} = 40353607$$

Step3: Eliminate the rational exponent

Raise both sides to the $\frac{4}{9}$ power.
$$x = 40353607^{\frac{4}{9}}$$
Note that $40353607 = 7^9$, so substitute this in:
$$x = (7^9)^{\frac{4}{9}}$$
$$x = 7^{9 \times \frac{4}{9}} = 7^4$$

Step4: Calculate the final value

Compute $7^4$.
$$7^4 = 7 \times 7 \times 7 \times 7 = 2401$$

Answer:

$\boldsymbol{2401}$