Find the positive solution of the equation. 3x^((2)/(5))+8=200 Answer:

Isolate x Term: First, we need to isolate the term containing the variable x on one side of the equation. Subtract 8 from both sides of the equation to get 3x^(2/5) alone on one side. 3x^(2/5) + 8 - 8 = 200 - 8 3x^(2/5) = 192Divide by 3: Next, we divide both sides of the equation by 3 to solve for x^(2/5). (3x^(2/5)) / 3 = 192 / 3 x^(2/5) = 64Remove Exponent: Now, we need to get rid of the exponent (2/5). We can do this by raising both sides of the equation to the reciprocal of (2/5), which is (5/2). (x^(2/5))^(5/2) = 64^(5/2)Simplify Exponent: When we raise a power to another power, we multiply the exponents. In this case, (2/5) * (5/2) = 1, so the left side simplifies to x. x = 64^(5/2)Calculate Result: To simplify 64^(5/2), we first find the square root of 64, which is 8, and then raise it to the power of 5. x = (8^2)^(5/2) x = 8^5Now we calculate 8 raised to the power of 5. 8^5 = 8 * 8 * 8 * 8 * 8 8^5 = 32768

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Find the positive solution of the equation.

3x^((2)/(5))+8=200
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Find the positive solution of the equation. $\newline$ $3 x^{\frac{2}{5}}+8=200$ $\newline$ Answer:

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Q. Find the positive solution of the equation.

\newline

3 x^{\frac{2}{5}}+8=200

\newline

Answer:

Isolate x Term: First, we need to isolate the term containing the variable $x$ on one side of the equation. $\newline$ Subtract $8$ from both sides of the equation to get $3x^{(2/5)}$ alone on one side. $\newline$ $3x^{(2/5)} + 8 - 8 = 200 - 8$ $\newline$ $3x^{(2/5)} = 192$
Divide by $3$ : Next, we divide both sides of the equation by $3$ to solve for $x^{2/5}$ . $\newline$ $\frac{3x^{2/5}}{3} = \frac{192}{3}$ $\newline$ $x^{2/5} = 64$
Remove Exponent: Now, we need to get rid of the exponent $(\frac{2}{5})$ . We can do this by raising both sides of the equation to the reciprocal of $(\frac{2}{5})$ , which is $(\frac{5}{2})$ . $\newline$ $(x^{\frac{2}{5}})^{\frac{5}{2}} = 64^{\frac{5}{2}}$
Simplify Exponent: When we raise a power to another power, we multiply the exponents. In this case, $(\frac{2}{5}) \times (\frac{5}{2}) = 1$ , so the left side simplifies to $x$ . $x = 64^{\frac{5}{2}}$
Calculate Result: To simplify $64^{5/2}$ , we first find the square root of $64$ , which is $8$ , and then raise it to the power of $5$ . $\newline$ $x = (8^2)^{5/2}$ $\newline$ $x = 8^5$
Calculate Result: To simplify $64^{\frac{5}{2}}$ , we first find the square root of $64$ , which is $8$ , and then raise it to the power of $5$ .
$x = (8^2)^{\frac{5}{2}}$
$x = 8^5$ Now we calculate $8$ raised to the power of $5$ .
$8^5 = 8 \times 8 \times 8 \times 8 \times 8$
$8^5 = 32768$