Final answer:
To find the values of m and n in the equation, match the exponents of x and y on both sides, then multiply the found values to get nm.
Step-by-step explanation:
The question involves finding the values of m and n in the equation x³⁴(√y/x)y⁵₈ = xᵐyⁿ. To solve for m and n, we need to match the exponents of x and y on both sides of the equation. The left side can be expressed as x raised to the power of ³⁴ times y raised to the power of ⁵₈. The square root of y/x is y to the power of 1/2 divided by x to the power of 1/2. Combining these, we match the exponents of x and y on both sides of the equation to find m and n.
Once m and n are found, calculating nᵐ is straightforward. It involves multiplying the found values of n and m.