5m^4/3(m^1/3*2n^1/8)
remember when multiplying powers of the same base we add the exponents
5m^4/3(m^1/3*2n^1/8)
= 10 m^(4/3) n^(1/8)
Hmmm. I get
10 m^(5/3) n^(1/8)
To simplify the expression 5m^4/3(m^1/3*2n^1/8), we can follow the order of operations (PEMDAS/BODMAS) and simplify each part separately.
Step 1: Simplify the expression within the parentheses.
Inside the parentheses, we have m^1/3 * 2n^1/8.
To simplify this, we multiply the coefficients (2) and the variables with the same bases (m and n), but different exponents (1/3 and 1/8).
m^1/3 * m^0 * 2 * n^1/8 can be rewritten as:
2m^(1/3 + 0) * n^1/8
2m^1/3 * n^1/8
Step 2: Apply the exponent rule to combine like terms.
Now, we multiply the coefficients (5 and 2), and combine the exponents with the same bases (m and n).
5m^4/3 * 2m^1/3 * n^1/8 can be rewritten as:
10m^(4/3 + 1/3) * n^1/8
Simplifying the exponents further:
10m^(4/3 + 1/3) equals 10m^(5/3), which means we add the exponents when multiplying.
n^1/8 remains the same.
Step 3: Finalize the expression.
After simplifying inside the parentheses, we are left with the expression:
10m^(5/3) * n^(1/8).
Therefore, 5m^4/3(m^1/3*2n^1/8) simplifies to 10m^(5/3) * n^(1/8).