Question

Simplify. ((m⁻³)n⁻²p⁵/(m⁻¹n))⁴. Write your answer using only positive exponents.

Answer 1

The simplified expression is p20/(m8n12) after applying the rules of exponents, including the quotient rule and the power rule, to get positive exponents only.

Step-by-step explanation:

To simplify the given expression ((m-3)n-2p5/(m-1n))4 and write it using only positive exponents, we need to apply the rules of exponents step by step:

1. First, simplify the expression inside the parentheses by applying the quotient rule of exponents, which states that when dividing like bases you subtract the exponents: m-3-(-1) and n-2-1.
2. Then you will get (m-2n-3p5)4.
3. Next, distribute the exponent of 4 to each factor inside the parentheses, which means multiplying the exponents: m-8, n-12, and p20.
4. The simplified result is m-8n-12p20.
5. Finally, to express the answer with positive exponents, take the reciprocals of the factors with negative exponents: m8 and n12.
6. The final answer is p20/(m8n12).