Simplify the expression: Please helllppp

Simplify each exponential expression using the properties of exponents and match it to the correct answer.

saveliy_v [14]

1) (2 $\times$ 3^-2)^3 (5 $\times$ 3^2)^2 / (3^-2)(5 $\times$ 2)^2 = 2

2) (3^3) (4^0)^2 (3 $\times$ 2)^-3 (2^2) = 1/2

3) (3^7 $\times$ 4^7) (2 $\times$ 5)^-3 (5)^2 / (12^7) (5^-1) (2^-4) = 2

4) (2.3)^-1 (2^0) / (2.3)^-1 = 1

<u>Step-by-step explanation</u>:

Step 1 :

(2 $\times$ 3^-2)^3 (5 $\times$ 3^2)^2 / (3^-2)(5 $\times$ 2)^2

⇒ (2^3) (3^-6) (5^2) (3^4) / (3^-2) (10^2)

⇒ (2.2^2.5^2) (3^-6.3^4) / (3^-2) (10^2)

⇒ (2)(10^2) (3^-2) / (3^-2) (10^2)

⇒ 2

Step 2 :

(3^3) (4^0)^2 (3 $\times$ 2)^-3 (2^2)

Any number with power 'zero' is 1.

⇒ (3^3) (1^2) (3^-3) (2^-3) (2^2)

⇒ (2^(-3+2))

⇒ 2^-1 = 1/2

Step 3 :

(3^7 $\times$ 4^7) (2 $\times$ 5)^-3 (5)^2 / (12^7) (5^-1) (2^-4)

⇒ (12^7) (2^-3) (5^-3) (5^2) / (12^7) (5^-1) (2^-4)

⇒ (2^-3) (5^(-3+2)) / (5^-1) (2^-4)

⇒ (2^-3) (5^-1) / (5^-1) (2^-4)

⇒ 1 / (2^-1)

⇒ 2

Step 4 :

(2.3)^-1 (2^0) / (2.3)^-1

⇒ (2^0)

⇒ Any number with power 'zero' is 1

⇒ 1

8 0

3 years ago

Sole in quadratic equation<br> 2x² + 3x + 8=0

olga_2 [115]

That the answer for it

3 0

3 years ago

a triangle has area 49.5 cm^2. if the base of the triangle is 9 cm, what is the height of the triangle

Anika [276]

Area of a triangle = (height * base ) / 2

height = (Area * 2) / base
height = (49.5 * 2) / 9
height = 99 / 9
height = 10 cm²

3 0

3 years ago

In a group of college students, the ratio of men to women is 3:1 (i.e., 3 to 1). In a recent survey, 40% of the men in this grou

katovenus [111]

Answer:

0.3875

Step-by-step explanation:

Given that in a group of college students, the ratio of men to women is 3:1 (i.e., 3 to 1). In a recent survey, 40% of the men in this group selected hiking as their favorite outdoor activity whereas 35% of the women in the group selected hiking as their favorite outdoor activity

From the above information we find that

P(Men) = 0.75 and P(women) = 0.25 (since men:women = 3:1)

Out of men prob for not selecting hiking as their favorite outdoor activity

$=1-0.6 = 0.4$

Out of women prob for not selecting hiking as their favorite outdoor activity

$=1-0.35 = 0.65$

Prob for a randomly selected person that hiking is not his/her favorite outdoor activity = Prob (man and not selected activitiy) + P(women and not selected activity) (since men and women are mutually exclusive and exhaustive)

= $0.75(0.4)+0.25(0.35)\\= 0.30+0.0875\\\\=0.3875$

6 0

3 years ago

Please help me, I will give brainliest! :D

solong [7]

Answer:

Sorry i dont know but need the points

Step-by-step explanation:

3 0

2 years ago