Answer :

To solve the equation [tex]\(9.7 x^{\frac{2}{3}} = 38.8\)[/tex], follow these steps:

1. Isolate [tex]\(x^{\frac{2}{3}}\)[/tex]:
- Divide both sides of the equation by 9.7 to isolate [tex]\(x^{\frac{2}{3}}\)[/tex].
- [tex]\[ x^{\frac{2}{3}} = \frac{38.8}{9.7} = 4 \][/tex]

2. Solve for [tex]\(x\)[/tex]:
- To solve for [tex]\(x\)[/tex], raise both sides of the equation to the power of [tex]\(\frac{3}{2}\)[/tex] to undo the [tex]\(\frac{2}{3}\)[/tex] exponent.
- [tex]\[ x = (4)^{\frac{3}{2}} \][/tex]

3. Calculate [tex]\(x\)[/tex]:
- [tex]\[ x = \sqrt{4^3} = \sqrt{64} = 8 \][/tex]

4. Check the solution:
- Substitute [tex]\(x = 8\)[/tex] back into the original equation to verify that it satisfies the equation.
- Calculate the left side:
[tex]\[ 9.7 \times (8)^{\frac{2}{3}} = 9.7 \times 4 = 38.8 \][/tex]
- The left side equals the right side of the original equation, confirming that [tex]\(x = 8\)[/tex] is indeed the correct solution.

Therefore, the solution to the equation [tex]\(9.7 x^{\frac{2}{3}} = 38.8\)[/tex] is [tex]\(x = 8\)[/tex].

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Rewritten by : Barada