Question

find 16 to the power of 3/2​

Answer 1

Answer:

64

Step-by-step explanation:

16^3/2

= (4^2)^3/2

= 4^3 (cancellation of 2 and 2)

= 64

Answer 2

$\displaystyle \sf {(16)}^{ \frac{3}{2} } = \bf 64$

Given :

$\displaystyle \sf {(16)}^{ \frac{3}{2} }$

To find :

The value of the expression

Formula Used :

We are aware of the formula on indices that

$\displaystyle \sf{ { ({a}^{m} )}^{n} = {a}^{mn} }$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf {(16)}^{ \frac{3}{2} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf {(16)}^{ \frac{3}{2} }$

$\displaystyle \sf = {( {4}^{2} )}^{ \frac{3}{2} }$

$\displaystyle \sf = {4}^{ (2 \times \frac{3}{2} )} \: \: \: \bigg[ \: \because \: { ({a}^{m} )}^{n} = {a}^{mn} \: \bigg]$

$\displaystyle \sf = {4}^{3}$

$\displaystyle \sf = 64$

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