Question

question
find the positive solution of the equation.
$8x^{\frac{9}{4}} + 21 = 322828877$

Explanation:

Step1: Isolate the variable term

Subtract 21 from both sides.
$$8x^{\frac{9}{4}} = 322828877 - 21$$
$$8x^{\frac{9}{4}} = 322828856$$

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

Divide both sides by 8.
$$x^{\frac{9}{4}} = \frac{322828856}{8}$$
$$x^{\frac{9}{4}} = 40353607$$

Step3: Eliminate the rational exponent

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

Step4: Calculate the final value

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

Answer:

$2401$