Question

question
find the positive solution of the equation.
$8x^{\frac{8}{5}} - 21 = 13436907$

Explanation:

Step1: Isolate the variable term

Add 21 to both sides of the equation.
$$8x^{\frac{8}{5}} = 13436907 + 21$$
$$8x^{\frac{8}{5}} = 13436928$$

Step2: Solve for $x^{\frac{8}{5}}$

Divide both sides by 8.
$$x^{\frac{8}{5}} = \frac{13436928}{8}$$
$$x^{\frac{8}{5}} = 1679616$$

Step3: Eliminate the rational exponent

Raise both sides to the power of $\frac{5}{8}$ (the reciprocal of $\frac{8}{5}$).
$$x = 1679616^{\frac{5}{8}}$$

Step4: Simplify the radical expression

First, rewrite 1679616 as $6^8$ (since $6^8 = 6\times6\times6\times6\times6\times6\times6\times6 = 1679616$).
$$x = (6^8)^{\frac{5}{8}}$$
Use the exponent rule $(a^m)^n = a^{m\times n}$:
$$x = 6^{8\times\frac{5}{8}} = 6^5$$
$$x = 7776$$

Answer:

$7776$