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Colt1911 [192]
3 years ago
10

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

Mathematics
1 answer:
Inessa05 [86]3 years ago
8 0
<h3>Answer:</h3>

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

<h3>Explanation:</h3>

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)

_____

<em>Where the rule comes from</em>

An exponent sigifies <em>repeated multiplication</em>. 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.

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Answer:

t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322

Step-by-step explanation:

We have a sample of size n = 35, \bar{x} = 92 and s = 5. As we want to construct a 95% confidence interval to estimate the value of the true population mean \mu, we should use the pivotal quantity given by T = \frac{\bar{X}-\mu}{S/\sqrt{n}} which comes from the t distribution with n - 1 = 35 - 1 = 34 degrees of freedom. Besides we should use the t-value t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322, i.e., regarding the t-distribution with 34 degrees of freedom, we have an area of 0.025 above 2.0322 and below the probability density function. The rationale behind this is that P(-2.0322\leq T\leq 2.0322) = 0.95 because of the simmetry of the t distribution.

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2 years ago
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