Question

(2^1/2 × 3^1/3 × 4^1/4)/(10^-1/5 × 5^3/5) ÷ (3^4/3 × 5^-7/5)/(4^3/5 × 6) = 10 PROVE THAT

Answer 1

Given: The correct term is (2^1/2 × 3^1/3 × 4^1/4)/(10^-1/5 × 5^3/5) ÷ (3^4/3 × 5^-7/5)/(4^-3/5 × 6) = 10

To find: Prove the above term.

Solution:

• Now we have given:

  (2^1/2 × 3^1/3 × 4^1/4)/(10^-1/5 × 5^3/5) ÷ (3^4/3 × 5^-7/5)/(4^-3/5 × 6) = 10

• Lets consider LHS, we have:

  (2^1/2 × 3^1/3 × 4^1/4)/(10^-1/5 × 5^3/5) / (3^4/3 × 5^-7/5)/(4^-3/5 × 6)

• Rewriting the equation in simplifies form, we get:

  (2^1/2 × 3^1/3 × 2^1/2)/(10^-1/5 × 5^3/5) / (3^4/3 × 5^-7/5)/(2^-6/5 × 3 × 2)

  (2 × 3^1/3)/(5^-1/5 × 2^-1/5 × 5^3/5) / (3^4/3 × 5^-7/5)/(2^-6/5 × 3 × 2)

• Now reciprocating denominator and multiplying it to numerator, we get:

   (2 × 3^1/3) x (2^-6/5 × 3 × 2) / (5^-1/5 × 2^-1/5 × 5^3/5) x (3^4/3 × 5^-7/5)

• Now taking the power of common base together, we get:

   2^(2-6/5) x 3^(1+1/3) / 5^(-1/5+3/5-7/5) x 2^(-1/5) x 3^(4/3)

   2^(4/5) x 3^(4/3) / 5^(-5/5) x 2^(-1/5) x 3^(4/3)

   2^(4/5 +1/5) x 3^(4/3 - 4/3) / 5^-1

   2^(5/5) x 5

   2^1 x 5

   10

Answer:

So from above solution we proved that :

(2^1/2 × 3^1/3 × 4^1/4)/(10^-1/5 × 5^3/5) ÷ (3^4/3 × 5^-7/5)/(4^-3/5 × 6) = 10

Answer 2

Answer:

10

Step-by-step explanation:

So ,

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