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Answer:
(b) p^(m+n)
Step-by-step explanation:
The rule for exponents is ...
(a^b)(a^c) = a^(b+c)
Here, you have a=p, b=m, c=n, so the product is ...
(p^m)(p^n) = p^(m+n)
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Additional comment
I find it useful to remember that an exponent signifies repeated multiplication.
p × p = p² . . . . . the exponent of 2 means p is a factor 2 times in the product
p × p × p = p³ . . . the exponent 3 means p is a factor 3 times in the product
Now, look at what happens when I multiply one of these by the other:
(p×p) × (p×p×p) is a product with p being a factor 2+3 = 5 times
Using exponent notation for the repeated multiplication, this is ...
[tex]p^2\times p^3=p^{2+3}=p^5[/tex]
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This "repeated multiplication" idea makes it relatively simple to understand other rules of exponents. When we divide, we cancel factors, so the exponents subtract. When we raise to a power, we multiply the number of factors, so the exponents multiply.
[tex]\dfrac{p\times p\times p}{p\times p}=p\ \Longleftrightarrow\ \dfrac{p^3}{p^2}=p^{3-2}=p^1=p\\\\(p\times p)^3=(p\times p)\times(p\times p)\times(p\times p)=p^6\ \Longleftrightarrow\ (p^2)^3=p^{2\times3}=p^6[/tex]
