Question

the value of z is given by the following z^z√z=(z√z)^z


plz answer this question fastly.........​

Answer 1

Step-by-step explanation:

the answer to this question is in a pic... hope u understand

Answer 2

Answer:

Required value of z is $2 \frac{1}{4}$

Step-by-step explanation:

Given,

${z}^{(z \sqrt{z} )} = {(z \sqrt{z} )}^{z} ....(1)$

We want to find value of z.

We know,

$\sqrt{x} = {x}^{ \frac{1}{2} }$

So from (1),

${z}^{(z \times {z}^{ \frac{1}{2}) } } = {z}^{z} \times { \sqrt{z} }^{z} \\ {z}^{ {z}^{1 + \frac{1}{2} } } = {z}^{z} \times {z}^{ \frac{1}{2}^{z} } \\ {z}^{ {z}^{ \frac{3}{2} } } = {z}^{z} \times {z}^{ \frac{z}{2} } \\ {z}^{ {z}^{ \frac{3}{2} } } = {z}^{z + \frac{z}{2} }$

${z}^{ \frac{3}{2} } = \frac{3z}{2}$

$\frac{ {z}^{ \frac{3}{2} } }{z} = \frac{3}{2} \\ {z}^{ \frac{3}{2} - 1 } = \frac{3}{2} \\ {z}^{ \frac{1}{2} } = \frac{3}{2} \\ { {z}^{ \frac{1}{2} } }^{2} = { (\frac{3}{2}) }^{2} \\ z = \frac{9}{4} \\ z = 2 \frac{1}{4}$

Here applied formulas are,

${x}^{a} \times {x}^{b} = {x}^{a + b}$

${x}^{ {y}^{z} } = {x}^{y \times z}$

This is a problem of Power of indices .

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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