Use the rules of exponents to evaluate or simplify.write without negative exponents. 1/4^-2=?
1 answer:
9514 1404 393
Answer:
4² = 16
Step-by-step explanation:
The applicable rule of exponents is ...
1/a^-b = a^b
So, ...
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<em>Additional comment</em>
If you were to evaluate this using the Order of Operations, you would evaluate the exponent first:
1/4^-2 = 1/(1/16)
Then, you would do the division.
1/(1/16) = 16
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We sometimes find it convenient to manipulate exponential terms to the form with the smallest positive exponents before we begin the evaluation.
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Part A
The sequence is geometric because the y values are doubling each time
4*2 = 8
8*2 = 16
16*2 = 32
The common ratio is r = 2.
<h3>Answer: Geometric</h3>=======================================================
Part B
The recursive rule here would be
The first line says that "the first term is 4"
The second line says "the nth term is found by multiplying 2 by the previous (n-1) term". In other words, double any term to get the next term.
The fourth term is 32 which doubles to 64 and that's the fifth term. So the point (5,64) is on this exponential curve.
Answer: She takes <u>64 minutes</u> to complete station 5
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Part C
We see that a = 4 is the first term and r = 2 is the common ratio.
The explicit nth term formula is a(r)^(n-1) which becomes 4(2)^(n-1)
Plugging in the value n = 8 leads to
4(2)^(n-1)
4(2)^(8-1)
4(2)^7
4(128)
512
You can use the method shown in part B to keep doubling each term until you arrive at the 8th term. This is one way to confirm the answer.
<h3>Answer: 512 minutes</h3>