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2 years ago

7

In 2005, a Nevada silver mine exported 200 tons of silver. In 2008, as the silver supply became exhausted, it only exported 25 t

ons of silver. What is the rate of change of the mine’s silver output?

1 answer:

yulyashka [42]2 years ago

7 0

To obtain the rate of change of mine's silver output, subtract the number of silver exported on 2005 from that on 2008. From the given, from 2005 to 2008, which is a span of 3 years, the exported silver decreased by 175 tons. Thus, the rate of change is equal to -175 tons per 3 years.

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2 years ago

Simplify LaTeX: \Large\frac{-4^{6} \cdot 4^{2}}{4^{4}}

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⇨ The value of this <u>simplified expression</u> = -4096/1 or -4096.

<h3> </h3>

To solve this expression, just multiply the power base by how many times indicate the exponent, and then divide the numerator and denominator of the fraction by the same number.

Power or potentiation is a multiplication in equal factors, where there are <em>terms responsible</em> for obtaining the final result. An potency is given by $\large \sf a^{n}.$ The terms of a power are:

<h3> </h3>

Base
Exponent
equal factors
power

<h3> </h3>

✏️ <u>Resolution/Answer</u>:

$\\ \large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=\\\\$

Multiply the powers of the numbers at numerator of the fraction, with the base <em>being multiplied by how many times</em> to indicate the exponent.

$\\\large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=$

$\large \sf \dfrac{-4\cdot4\cdot4\cdot4\cdot4\cdot4\cdot 4^{2}}{4^{4}}=$

$\large \sf \dfrac{-4\cdot4\cdot4\cdot4\cdot16\cdot 4^{2}}{4^{4}}=$

$\large \sf \dfrac{-4\cdot4\cdot16\cdot16\cdot 4^{2}}{4^{4}}=$

$\large \sf \dfrac{-16\cdot16\cdot16\cdot 4^{2}}{4^{4}}=$

$\large \sf \dfrac{-16\cdot16\cdot16\cdot 4\cdot4}{4^{4}}=$

$\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4^{4}}=\\\\$

<em>Multiply </em>the power at denominator of the fraction:

$\\\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4^{4}}=$

$\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4\cdot4}=$

$\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{16}=\\\\$

<em>Multiply </em>the numerator numbers together:

$\\\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{16}=$

$\large \sf \dfrac{-16\cdot16\cdot 256 }{16}=$

$\large \sf \dfrac{-256\cdot 256 }{16}=$

$\large \sf \dfrac{- 65536 }{16}=\\\\$

Simplify the fraction by number 16:

$\\\large \sf \dfrac{- 65536 }{16}=$

$\large \sf \dfrac{- 65536 \div16}{16\div16}=$

${\orange{\boxed{\boxed{\pink {\large \displaystyle \sf { \frac{-4096}{1} \ or \ -4096 }}}}}} \\\\\\$

So this expression in its simplified form = -4096/1 or -4096.

${\orange{\boxed{\boxed{\pink {\large \displaystyle \sf { \frac{-4096}{1} \ or \ -4096 }}}}}}\\\\$

★ Hope this helps! ❤️

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Step-by-step explanation:

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