Final answer:
To solve the given equation for m, multiply both sides by 8 to isolate m raised to the 5/3 power, take both sides to the reciprocal of 5/3 power (3/5), and calculate the value, which gives m ≈ 2.2974.
Step-by-step explanation:
To solve for m in the equation (m⁵/³)/8 = 1/2, we follow these steps:
- Multiply both sides by 8 to isolate the m term: m⁵/³ = 4.
- Now we want to get m by itself, which means we need to deal with the fractional exponent. We can raise both sides of the equation to the reciprocal of 5/3 power, which is 3/5, to cancel out the exponent on m. This is the same as taking the 5th root of both sides and then raising to the power of 3: m = 4¹/³.
- Calculate the fifth root of 4, which is approximately 1.3195, and then raise this result to the third power: m ≈ 1.3195³.
- Finally, we find m ≈ 2.2974, but since we started with a simple fraction, we should express m as a fraction or a simplified radical form if possible.
In summary, the value for m is approximately 2.2974 when solved algebraically.