Question

This is really hard please help

Answer 1

9514 1404 393

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 ...

  $p^2\times p^3=p^{2+3}=p^5$

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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.

  $\dfrac{p\times p\times p}{p\times p}=p\ \Longleftrightarrow\ \dfrac{p^3}{p^2}=p^{3-2}=p^1=p\\\\(p\times p)^3=(p\times p)\times(p\times p)\times(p\times p)=p^6\ \Longleftrightarrow\ (p^2)^3=p^{2\times3}=p^6$