Whoever answers first gets brainliest match each exponential expression on the left with the rational number on the right. (5^3/2)^-2/3 a. 7 (256^0.5)1.25 b. 10,000 (81^1/6)^3/2 c. 32 (1024^.03)^20 d. 64 (1000^4/7)^7/3 e. 0.2 (49^5/2)^0.2 f.

(5^3/2)^-2/3 = 0.2 ⇒ E

(256^0.5)^1.25 = 32 ⇒ C

(81^1/6)^3/2 = 3 ⇒ F

(1024^0.03)^20 = 64 ⇒ D

(1000^4/7)^7/3 = 10,000 ⇒ B

(49^5/2)^0.2 = 7 ⇒ A

Step-by-step explanation:

* Lets explain how to solve the problem

- If we have base x to a power n and all to the power of m then we

 multiply the two powers to be one power on the base

- [(x^n)^m] = x^(nm)

* Lets solve the problem

∵

∴ (5^3/2)^-2/3 = 0.2 ⇒ E

∵

∵ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^8

∴

∴ (256^0.5)^1.25 = 32 ⇒ C

∵

∵ 81 = 3 × 3 × 3 × 3 = 3^4

∴

∴ (81^1/6)^3/2 = 3 ⇒ F (answer F must be 3 not 0.333)

∵

∵ 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^10

∴

∴ (1024^0.03)^20 = 64 ⇒ D

∵

∵ 1000 = 10 × 10 × 10 = 10³

∴

∴ (1000^4/7)^7/3 = 10,000 ⇒ B

∵

∴ (49^5/2)^0.2 = 7 ⇒ A

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

its totaly b

your welcome btw