Question

what is the value of(2)³/²​

Answer 1

Answer:

8²

64

please check if this is right or not I am not confirmed if this is right .

Caution: please check one more time

Answer 2

Answer:

The value of ${2}^{ \frac{3}{2} }$ is 2√2.

Step-by-step explanation:

Given expression is ${2}^{ \frac{3}{2} }$

We want to find value of this.

Now we can write

$\frac{3}{2} = 1 + \frac{1}{2}$

So,

${2}^{1 + \frac{1}{2} }$

We know,

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

So,

${2}^{1 + \frac{1}{2} } \\ = {2}^{1} \times {2}^{ \frac{1}{2} } \\ = 2 \times \sqrt{2} \\ = 2 \sqrt{2}$

So, value of ${2}^{ \frac{3}{2} }$ is 2√2.

Here applied two formulas are

${x}^{a + b} = {x}^{a} \times {x}^{b} \\ and \: \sqrt{x} = {x}^{ \frac{1}{2} }$

This is a problem of Power of indices.

Some important formulas of Power of indices:

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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