Answer:
(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
∵ [tex](5^{\frac{3}{2}})^{\frac{-2}{3}}=5^{(\frac{3}{2})(\frac{-2}{3})}=5^{-1}=\frac{1}{5}=0.2[/tex]
∴ (5^3/2)^-2/3 = 0.2 ⇒ E
∵ [tex](256^{0.5})^{1.25}=256^{(0.5)(1.25)}=256^{\frac{5}{8}}[/tex]
∵ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^8
∴ [tex]256^{\frac{5}{8}}=(2^{8})^{\frac{5}{8}}=2^{(8)(\frac{5}{8})}=2^{5}=32[/tex]
∴ (256^0.5)^1.25 = 32 ⇒ C
∵ [tex](81^{\frac{1}{6}})^{\frac{3}{2}}=81^{(\frac{1}{6})(\frac{3}{2})}=81^{(\frac{3}{12})}=3^{\frac{1}{4} }[/tex]
∵ 81 = 3 × 3 × 3 × 3 = 3^4
∴ [tex]81^{\frac{1}{4}}=(3^{4})^{\frac{1}{4}}=3^{(4)(\frac{1}{4})}=3[/tex]
∴ (81^1/6)^3/2 = 3 ⇒ F (answer F must be 3 not 0.333)
∵ [tex](1024^{0.03})^{20}}=1024^{(0.03)(20)}=1024^{\frac{3}{5}}[/tex]
∵ 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^10
∴ [tex]1204^{\frac{3}{5}}=(2^{10})^{\frac{3}{5}}=2^{(10)(\frac{3}{5})}=2^{6}=64[/tex]
∴ (1024^0.03)^20 = 64 ⇒ D
∵ [tex](1000^{\frac{4}{7}})^{\frac{7}{3}}=1000^{(\frac{4}{7})(\frac{7}{3})}=1000^{\frac{4}{3}}[/tex]
∵ 1000 = 10 × 10 × 10 = 10³
∴ [tex]1000^{\frac{4}{3}}=(10^{3})^{\frac{4}{3}}=10^{(3)(\frac{4}{3})}=10^{4}=10,000[/tex]
∴ (1000^4/7)^7/3 = 10,000 ⇒ B
∵ [tex](49^{\frac{5}{2}})^{0.2}=49^{(\frac{5}{2})(0.2)}=49^{\frac{1}{2}}=7[/tex]
∴ (49^5/2)^0.2 = 7 ⇒ A
