Question

What is p^m ⋅ p^n equal to? p^m − n p^m + n p^m ⋅ n p^m ÷ n. please show work

Answer 1

Answer:

p^(m+n) . . . . . . . parentheses are required

Explanation:

The answer follows directly from the rules of exponents:

... (a^b)×(a^c) = a^(b+c)

Here, you have a=p, b=m, c=n, so

... (p^m)×(p^n) = p^(m+n)

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Where the rule comes from

An exponent sigifies repeated multiplication. That is ...

... p^3 = p·p·p . . . . . . . the exponent means p is a factor 3 times

... p^2 = p·p . . . . . . . . .the exponent means p is a factor 2 times

When we multiply these terms together, we have ...

... (p^3)×(p^2) = (p·p·p)×(p·p) = p·p·p·p·p = p^(2+3) = p^5

The number of times p is a factor of the product is the total of the number of times p is a factor in the factors of the product.