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Novay_Z [31]
2 years ago
7

Oct 13, 7:36:04 PM

Mathematics
1 answer:
nikklg [1K]2 years ago
8 0

Step-by-step explanation:

the remaining gas in the tank after driving for 2 hours = 9 - (2×2) = 9-4 = 5 gallons

after t hours = (9 - 2t) gallons

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If the expression $3^1 times 9^2 times 27^3 \times 81^4 is simplified to the form 3^n, what is the value of n?
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Answer:

n=30

Step-by-step explanation:

Given expression:

3^1\times 9^2\times 27^3\times 81^4

The given expression needs to be simplified to the form 3^n

Applying the exponents rule to simplify.

3^1\times 9^2\times 27^3\times 81^4

Writing all numbers as product of 3.

⇒ 3^1\times (3\times3)^2\times (3\times3\times3)^3\times (3\times3\times3\times3)^4

Writing each in exponents form.

⇒ 3^1\times (3^2)^2\times (3^3)^3\times (3^4)^4

Using power of a power rule [\ (a^x)^y=a^{xy}\ ]

⇒ 3^1\times 3^4\times 3^9\times 3^16

Using multiplication rule of exponents [\ a^x\times a^y=a^{x+y}\ ]

⇒ 3^{1+4+9+16}

⇒ 3^{30}

So we have 3^n=3^{30}

∴ n=30

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