What is p−m ÷ pn equal to? (5 points)
p−m + n
p−m ⋅ n
p−m − n
p−m ÷ n
p−m ÷ pn is equal to (p−m) ÷ n
To solve the expression p−m ÷ pn, we need to follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
Starting with the expression p−m ÷ pn, we can simplify it step by step:
Step 1: Simplify the exponents.
The exponent on the variable n is pn, which means n multiplied by itself p times. Since there is no exponent on p, we can simplify pn to n^p.
So, p−m ÷ pn becomes p−m ÷ n^p.
Step 2: Perform the division.
To divide p−m by n^p, we need to subtract the exponents of the variables.
Therefore, p−m ÷ n^p simplifies to p−m - p.
Step 3: Combine like terms.
Since p is being subtracted from p−m, we can rewrite p−m - p as -m.
Therefore, p−m ÷ pn is equal to -m.
Answer: -m
To find the value of p−m ÷ pn, you need to simplify the expression.
Step 1: Firstly, apply the exponentiation rule to pn, which dictates that when dividing exponents with the same base, you subtract the exponents. Therefore, pn can be simplified to p^(n-1).
Step 2: Now, substitute the simplified expression into p−m ÷ pn. This gives us p−m ÷ p^(n-1).
Step 3: Apply the division rule for exponents, which states that when dividing exponents with the same base, you subtract the exponents. Thus, p−m ÷ p^(n-1) can be rewritten as p^(1-m-n+1).
Step 4: Simplify the expression further by combining like terms. In this case, 1-m-n+1 simplifies to 2-m-n.
Finally, the simplified expression of p−m ÷ pn is p^(2-m-n).
Therefore, the answer to your question is p^(2-m-n).