Mathematics: 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.

Shape A is congruent to shape [ F ] as shown by a reflection across the y-axis and then a translation down [ 3 ] units. Shape B is congruent to shape [ D ] as shown by a reflection across the y-axis and then a translation down [ 2 ] units....

Whoever answers first gets brainliest match each

Ответ:

andrespiperderc

15.03.2022

Mathematics

(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

∵ $(5^{\frac{3}{2}})^{\frac{-2}{3}}=5^{(\frac{3}{2})(\frac{-2}{3})}=5^{-1}=\frac{1}{5}=0.2$

∴ (5^3/2)^-2/3 = 0.2 ⇒ E

∵ $(256^{0.5})^{1.25}=256^{(0.5)(1.25)}=256^{\frac{5}{8}}$

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

∴ $256^{\frac{5}{8}}=(2^{8})^{\frac{5}{8}}=2^{(8)(\frac{5}{8})}=2^{5}=32$

∴ (256^0.5)^1.25 = 32 ⇒ C

∵ $(81^{\frac{1}{6}})^{\frac{3}{2}}=81^{(\frac{1}{6})(\frac{3}{2})}=81^{(\frac{3}{12})}=3^{\frac{1}{4} }$

∵ 81 = 3 × 3 × 3 × 3 = 3^4

∴ $81^{\frac{1}{4}}=(3^{4})^{\frac{1}{4}}=3^{(4)(\frac{1}{4})}=3$

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

∵ $(1024^{0.03})^{20}}=1024^{(0.03)(20)}=1024^{\frac{3}{5}}$

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

∴ $1204^{\frac{3}{5}}=(2^{10})^{\frac{3}{5}}=2^{(10)(\frac{3}{5})}=2^{6}=64$

∴ (1024^0.03)^20 = 64 ⇒ D

∵ $(1000^{\frac{4}{7}})^{\frac{7}{3}}=1000^{(\frac{4}{7})(\frac{7}{3})}=1000^{\frac{4}{3}}$

∵ 1000 = 10 × 10 × 10 = 10³

∴ $1000^{\frac{4}{3}}=(10^{3})^{\frac{4}{3}}=10^{(3)(\frac{4}{3})}=10^{4}=10,000$

∴ (1000^4/7)^7/3 = 10,000 ⇒ B

∵ $(49^{\frac{5}{2}})^{0.2}=49^{(\frac{5}{2})(0.2)}=49^{\frac{1}{2}}=7$

∴ (49^5/2)^0.2 = 7 ⇒ A

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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.

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