Question

for x=5 and y=4 determine the value of following expression.

Refer the image for expression

Answer 1

Answer:

bro you question is rong

Answer 2

Correct Question

Determine the value of the following expression for x=5 and y=4

$\sqrt[9]{[(x^y)^{y - 1/y}]^{1/(y+1)}}$

Options

a) ∛5

b)  -∛5

c) 25

d)125

Answer

Therefore, the value of the expression is a) ∛5

Given

$\sqrt[9]{[(x^y)^{y - 1/y}]^{1/(y+1)}}$

x = 5 and y = 4

To Find

The value of the expression

Solution

$\sqrt[9]{[(x^y)^{y - 1/y}]^{1/(y+1)}}$

We know that x = 5 and y = 4

Therefore, putting this in the equation we get,

$\sqrt[9]{[(5^4)^{4 - 1/4}]^{1/(4+1)}}$

Now we will solve this expression step by step.

First, we will solve the outermost exponent i.e 1/(4 + 1)

This will give us 1/5. Hence the expression becomes,

$\sqrt[9]{[(5^4)^{4 - 1/4}]^{1/5}}$

now 4 - 1/4

= (16 - 1)/4

= 15/4

Putting this in the above expression gives us,

$\sqrt[9]{[(5^4)^{15/4}]^{1/5}}$

Now since there is a bracket between the two powers, we need to multiply them.

15/4 X 1/5

= 15/20

= 3/4

Hence we get the expression$\sqrt[9]{[(5^4)^{3/4}]}$

Now, just like before we will multiply the powers 4 and 3/4

Therefore, 4 X 3/4 = 12/4 = 3

Hence we get

$\sqrt[9]{5^3}$

= ∛5

Therefore, the value of the expression is a) ∛5

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