Simplify the expression m^0 * n^4 * m^0 * n^4 / m^-1 * n^-8 and express your answer using positive exponents.

Steps to Solve

1. Identify the expression to simplify The expression we need to simplify is

$$ \frac{m^0 n^4 \cdot m^0 n^4}{m^{-1} n^{-8}} $$

2. Apply the zero exponent rule Recall that any number to the power of zero is 1. Therefore,

$$ m^0 = 1 $$

So, the expression simplifies to

$$ \frac{1 \cdot n^4 \cdot 1 \cdot n^4}{m^{-1} n^{-8}} = \frac{n^4 \cdot n^4}{m^{-1} n^{-8}} $$

3. Combine the like terms in the numerator Now, we combine the terms in the numerator:

$$ n^4 \cdot n^4 = n^{4 + 4} = n^8 $$

Thus, we rewrite the expression as:

$$ \frac{n^8}{m^{-1} n^{-8}} $$

4. Simplify the expression Next, simplify the denominator by applying the negative exponent rule:

$$ m^{-1} = \frac{1}{m} \quad \text{and} \quad n^{-8} = \frac{1}{n^8} $$

So we have:

$$ \frac{n^8}{\frac{1}{m} \cdot \frac{1}{n^8}} = n^8 \cdot m \cdot n^8 = m \cdot n^{8 + 8} = m \cdot n^{16} $$

5. Final answer with positive exponents The final simplified expression, using only positive exponents, is:

$$ m n^{16} $$