Question

Please answer the following question step by step​

Answer 1

Given :-

³√(0.512/y) = ³√1000

To find :-

Find the value of y ?

Solution :-

Given that:

³√(0.512/y) = ³√1000

Since nth root a = a^1/n

=> (0.512/y)^1/3 = (1000)^1/3

On cubing both sides then

=> [(0.512/y)^1/3 ]³= [(1000)^1/3]³

=> (0.512/y)^3/3 = (1000)^3/3

Since (a^m)^n = a^mn

=> 0.512/y = 1000

=> 0.512 = 1000×y

=> 1000×y = 0.512

=> 1000×y = 512/1000

=> y = (512/1000)/1000

=> y = 512/(1000×1000)

=> y = 512/1000000

=> y = 0.000512

Therefore, y = 0.000512

Answer:-

The value of y for the given problem is 0.000512

Check:-

If y = 0.000512 then

LHS = ³√(0.512/y)

=> ³√(0.512/0.000512)

=> ³√[(512/1000)/(512/1000000)]

=> ³√(1000000/1000)

=> ³√1000

=> RHS

=> LHS = RHS is true for y = 0.000512

Check :-

• (a^m)^n = a^mn

• nth root a = a^1/n

Answer 2

I think the following ll b the answer...

y = (2/25)^3 or 8/15625 or 0.000512