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Question: Refer to the attachment.
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NCERT IXth (Mathematics)
Topic: Number Systems
(Chapter : 1) ​

Answer 1

Answer:

Step-by-step explanation:

a = b^(2x)   ; b = c^(2y)   ;  c = a^(2z)

      Now,

        b = c^(2y)   , but c = a^(2z)

⇒  b = [a^(2z) ]^(2y)

        = a^(2z*2y)

        = a^(4zy)

  Now,

⇒ a = b^(2x)       , but b = a^(4zy)

⇒ a = [a^(4zy) ]^(2x)

⇒ a = a^(4zy * 2x)

⇒ a^1 = a^(8xyz)         {a =a^1}

          Bases are same, so

⇒ 1 = 8xyz

⇒ (1/8) = xyz

Answer 2

Given:-

• a = b^2x
• b = c^2y
• c = a^2z

To Prove: xyz = ⅛

Here,

a = b^2x

→ a = (c^2y)^2x [∵ b = c^2y]

→ a = c^4xy

Also,

c = a^2z

→ c = (c^4xy)^2z

[∵ a = c^4xy (Already Proved)]

→ c = c^8xyz

→ c¹ = c^8xyz

Since bases are same,

∴ 8xyz = 1

→ xyz = ⅛

☞ HENCE, PROVED.