Simplify. Express your answer using positive exponents. 4m^0 4m^−5

To simplify the expression ( 4m^0 cdot 4m^{-5} ), we can follow these steps:

1. Understand Exponents: The term ( m^0 ) equals 1 for any non-zero ( m ). Therefore, ( 4m^0 = 4 ).

2. Apply the Product of Powers Rule: When multiplying terms with the same base, you add the exponents. Here, we combine the two parts:

[

4 cdot (4m^{-5}) = 4 cdot 4 cdot m^{-5} = 16m^{-5}

]

3. Convert Negative Exponent to Positive: Recall that ( m^{-n} = frac{1}{m^n} ). Hence,

[

16m^{-5} = frac{16}{m^5}

]

So, the simplified expression is:

[

frac{16}{m^5}

]

This answer is expressed using positive exponents. Great job on wanting to simplify! If you have more questions or need further clarification, feel free to ask!