.[{(2)1/2 . (4)3/4 . (8)5/6 . (16)7/8 . (32)9/10} 4 ] 3/25 is?

Question

Answer

Calculation of [(2)1/2 . (4)3/4 . (8)5/6 . (16)7/8 . (32)9/10} 4 ] 3/25

Step 1: Simplifying the expression inside the brackets

To simplify the expression inside the brackets, we need to use the laws of exponents. Here's how we can do it:

2^(1/2) can be written as the square root of 2

4^(3/4) can be written as the fourth root of 4 cubed

8^(5/6) can be written as the sixth root of 8 to the power of 5

16^(7/8) can be written as the eighth root of 16 to the power of 7

32^(9/10) can be written as the tenth root of 32 to the power of 9

Therefore, the expression inside the brackets can be simplified as:

√2 . 4^(3/4) . 8^(5/6) . 16^(7/8) . 32^(9/10)

Step 2: Simplifying the expression outside the brackets

The expression outside the brackets is 4^(3/25). To simplify this, we can use the law of exponents that states: (a^m)^n = a^(m*n). Applying this law, we get:

4^(3/25) = (4^(1/25))^3

Step 3: Simplifying the entire expression

Now that we have simplified the expression inside and outside the brackets, we can combine them to get the final answer. Here's how we can do it:

[(2)1/2 . (4)3/4 . (8)5/6 . (16)7/8 . (32)9/10} 4 ] 3/25

= √2 . 4^(3/4) . 8^(5/6) . 16^(7/8) . 32^(9/10) . (4^(1/25))^3

= √2 . 4^(3/4) . 8^(5/6) . 16^(7/8) . 32^(9/10) . 4^(3/25)

= 2^(1/2) . 2^3 . 2^(5/3) . 2^(7/4) . 2^(9/5) . 2^(3/25)

= 2^[(1/2) + 3 + (5/3) + (7/4) + (9/5) + (3/25)]

= 2^[(225 + 3375 + 4500 + 7875 + 6750 + 225)/4500]

= 2^(23300/4500

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