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algol [13]
3 years ago
11

Simplify. this please​

Mathematics
2 answers:
frez [133]3 years ago
4 0

Answer: -125p12z18u3

Reason:

Square negative five twice, so: -5 x -5 x -5 = -125

The first squaring is -5 x -5, which is 25. The second squaring is 25 x (-5), which is - 125.

When it comes to the letters, they act like they are being multiplied.

(p4)3 = p12

(z6)3 = z18

(u)3 = u3

So the answer is -125p12z18u3.

Hope this helps! :)

katen-ka-za [31]3 years ago
3 0

First you have to know the "power rule." This is when there is an exponent outside the parentheses and some/all of the variables/numbers in the parentheses have exponents as well. What you do is multiply the outer exponent with each of the exponents inside the parentheses.

((-5)^{1*3} p^{4*3} z^{6*3} u^{1*3} )

(-5)^{3}p^{12}z^{18}u^{3}

-125p^{12}z^{18}u^{3}

Hope this helped!

~Just a girl in love with Shawn Mendes

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Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

(c) The amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720

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Compute the 5-hour decay factor as follows:

5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720

Thus, the 1-hour decay factor is 0.8720.

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The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)<em>ⁿ</em>

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

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{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}

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