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3 years ago

Simplify (4^3)^5 - - - - -

Mathematics

2 answers:

MissTica3 years ago

6 0

Answer:

$\large\boxed{(4^3)^5=4^{15}}$

Step-by-step explanation:

$\text{Use}\ (a^n)^m=a^{nm}\\\\(4^3)^5=4^{(3)(5)}=4^{15}$

Slav-nsk [51]3 years ago

5 0

Step-by-step explanation: Here we have the number (4^3)^5.

We can use the relationship: $(x^{a} )^{b} = x^{a*b}$

so our number can be written as: $(4^{3}) ^{5} = 4^{3*5} = 4^{15}$ .

But you can simplify it further!

we know that $4 = 2^{2}$ , then $4^{15} = (2^{2}) ^{15} = 2^{2*15} = 2^{30}$

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3 years ago

Nana has a water purifier that filters \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction of the contaminants each ho

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Given:

Nana has a water purifier that filters $\dfrac{1}{3}$ of the contaminants each hour.

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To find:

The function that gives the remaining amount of contaminants in kilograms, C(t), t hours after Nana started purifying the water.

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Let C(t) be the remaining amount of contaminants in kilograms after t hours.

Initial amount of contaminants = $\dfrac{1}{2}$

Decreasing rate is $\dfrac{1}{3}$ .

Using the exponential decay model:

$C(t)=C_0(1-r)^t$

where, $C_0$ is initial amount of contaminants, r is the decreasing rate and t is time in hours.

Substituting the values, we get

$C(t)=\dfrac{1}{2}(1-\dfrac{1}{3})^t$

$C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t$

Therefore, the required function is $C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t$ .

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3 years ago

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3 years ago

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