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3 years ago

An example of Power of a Power Property

1 answer:

3 0

Power of a power as applied to exponents is the following:

The power of a power is the product of the exponents, or

(x^a)^b = x^(ab)

For example
(5^2)^3=5^(2*3)=5^6=15625

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Find the value of the constant term in the expansion of x^4 (x+3/2x^2)^5

Nataly_w [17]

5 is the answer ok I'll explain

4 0

2 years ago

What is the mode of this data set 55 78 43 39 78 61 75 50 43 78

Rom4ik [11]

Mode means MOST. Which number is displayed the most?

39, 43, 43, 50, 55, 61, 75, <u>78, 78, 78</u>

Answer: 78

Note: I placed the data set into numerical order because it will help you to easily find the mode and also the median (middle number).

5 0

2 years ago

Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates

natali 33 [55]

The rule for a rotation by 180° about the origin is (x,y) -->(−x,−y)

So A(-3, 2) to A'(3, -2)

Answer:

A'(3, -2)

4 0

2 years ago

??????? Help please

Ad libitum [116K]

Step-by-step explanation:

Put the values of x = 6, y = -7 and z = 0.8 to the expressions:

a) 5x → 5(6) = 30

b) 3y → 3(-7) = -21

c) 10z → 10(0.8) = 8

4 0

3 years ago

Read 2 more answers

39-50 find the limit.<br> 41. <img src="https://tex.z-dn.net/?f=%5Clim%20_%7Bt%20%5Crightarrow%200%7D%20%5Cfrac%7B%5Ctan%206%20t

Katyanochek1 [597]

Write tan in terms of sin and cos.

$\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}$

Recall that

$\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1$

Rewrite and expand the given limand as the product

$\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)$

Then using the known limit above, it follows that

$\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}$

4 0

1 year ago