Question

question
find the positive solution of the equation.
$7x^{\frac{8}{7}} - 22 = 11757290$
answer attempt 1 out of 2

Explanation:

Step1: Isolate the variable term

Add 22 to both sides.
$$7x^{\frac{8}{7}} = 11757290 + 22$$
$$7x^{\frac{8}{7}} = 11757312$$

Step2: Solve for $x^{\frac{8}{7}}$

Divide both sides by 7.
$$x^{\frac{8}{7}} = \frac{11757312}{7}$$
$$x^{\frac{8}{7}} = 1679616$$

Step3: Eliminate the rational exponent

Raise both sides to the power of $\frac{7}{8}$.
$$x = (1679616)^{\frac{7}{8}}$$

Step4: Simplify the base

Note that $1679616 = 6^8$, substitute this in.
$$x = (6^8)^{\frac{7}{8}}$$
$$x = 6^{8 \times \frac{7}{8}}$$
$$x = 6^7$$

Step5: Calculate the final value

Compute $6^7$.
$$6^7 = 279936$$

Answer:

279936