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MariettaO [177]
2 years ago
8

Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

Mathematics
1 answer:
Paladinen [302]2 years ago
5 0

Answer:  a) 1024, b) 1, c) 64 and d) 0.125.

Step-by-step explanation:

Since we have given that

(a) (4^3)(4^2)

As we know that

a^m\times a^n=a^{m+n}

So, it becomes,

4^3\times 4^2=4^{3+2}=4^5=1024

(b) (\dfrac{1}{4})^2(4^2)

As we know that

a^{-m}=\dfrac{1}{a^m}

(\dfrac{1}{4})^2(4^2)=4^-2\times 4^2=4^{-2+2}=4^0=1

c) (4^6)1/2

As we know that

(4^6)^{\frac{1}{2}}\\\\=4^{\frac{6}{2}}\\\\=4^3\\\\=64

(d) [(8^{-1})(8^{\frac{2}{3}})]^3

As we know that

[(8^{-1})(8^{\frac{2}{3}})]^3\\\\=[8^{-1+\frac{2}{3}}]^3\\\\=[8^{\frac{-1}{3}}]^3\\\\=8^{-1}\\\\=\dfrac{1}{8}=0.125

Hence, a) 1024, b) 1, c) 64 and d) 0.125.

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Step-by-step explanation:

A

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3 years ago
In one month a store had 1,222 in sales but expenses were 2,345 how much money did the store lose in that month
dangina [55]
We simply need to subtract 1,222 from 2,345. Once we do that we get 1,223. Hope that helps! :)
6 0
3 years ago
Find the area of the polygon with vertices (1, 2) (1, -5) (5, -5) (5,2)
Svetradugi [14.3K]

Answer:

28 square units

Step-by-step explanation:

These vertices are written in the form of their x and y coordinates. Let

A=(1,2) ; B =(1,-5) ; C =(5, -5) ; D=(5,2)

The x points are 1, 1, 5, 5

The y points are 2,-5, -5, 2

The x extremes range from 1 to 5. The length  in-between is 5-1 = 4

The y extremes range from -5 to 2. The length  in-between is 2-(-5) = 7

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5 0
2 years ago
While visiting Wallawulla State​ Park, Joe approximated the angle of elevation to the top of a mound to be 40 degrees . After wa
katen-ka-za [31]

Answer:

Height of mound = 794 ft

Step-by-step explanation:

To illustrate the angle of elevation and distance, i have drawn it and attached below.

Now, from my diagram;

h = the height of the mound

At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"

So, by triangle definition,

tan(40°) = h/x

And so;

h = x tan40

h = 0.8391x  - - - - (eq 1)

At his second point of the trip to the foot of the mound, Joe is now,

"(x - 450) ft" from the foot of the mound.

Thus, his angle of elevation is 40 + 18 = 58°.

So, by triangle definition,

tan(58°) = h/(x - 450)

h = (x - 450)•(tan(58°))

h = 1.6003(x - 450)

h = 1.6003x - 720.135   - - - - -(eq2)

To get the height(h) of the mound, let's equate (eq1) to (eq2).

0.8391x = 1.6003x - 720.135

1.6003x - 0.8391x = 720.135

0.7612x = 720.135

x = 720.135/0.7612

x = 946.0523 ft

Let's put this value for x in eq (1);

h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft

4 0
3 years ago
One canned juice drink is 25​%orange​ juice; another is 10​%orange juice. how many liters of each should be mixed together in or
sertanlavr [38]
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Drink 1:    x            .25      =      .25x
Drink 2:   15 - x      .10      =      .10(15 - x)
Mixture:  15            .21     =       .25x + .10(15 - x)

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                           3.15      =     .15x + 1.5
                           1.65      =     .15x
                               11     =       x

Drink 1 (25%) is 11 liters
Drink 2 (10%) is 15 - 11 = 4 liters
6 0
3 years ago
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