Question

{(root3/9)^5/2 (9/3root3)^7/2}*9

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The answer is 27

GIVEN

Mathematical expression;

$( \frac{ \sqrt{3} }{9} )^{ \frac{5}{2} } \times ( \frac{9}{ \sqrt{3} } ) ^{ \frac{7}{2} } \times 9$

TO FIND

To simplify the given expression;

SOLUTION

We can simply solve the above problem as follows;

We are given an expression;

$( \frac{ \sqrt{3} }{9} )^{ \frac{5}{2} } \times ( \frac{9}{ \sqrt{3} } ) ^{ \frac{7}{2} } \times 9$

We can write √3 as 3¹/², 9 as 3²

Therefore,

$( \frac{ {3}^{ \frac{1}{2} } }{ {3}^{2} } )^{ \frac{5}{2} } \times ( \frac{ {3}^{2} }{ {3}^{ \frac{1}{2} } } ) ^{ \frac{7}{2} } \times 9$

We know that,

mᵃ/mᵇ = mᵃ⁻ᵇ

Therefore,

$= ( {3}^{ \frac{1}{2} - 2 } )^{ \frac{5}{2} } \times (3^{2 - \frac{1}{2} } )^{ \frac{7}{2} } \times {3}^{2}$

$= (3^{ - \frac{3}{2} })^{ \frac{5}{2} } \times (3^{\frac{3}{2} })^{ \frac{7}{2} } \times {3}^{2}$

We know that,

(mᵃ)ᵇ = mᵃˣᵇ

Therefore,

$= {3}^{ - \frac{3}{2} \times \frac{5}{2} } \times {3}^{ \frac{3}{2} \times \frac{7}{2} } \times {3}^{2}$

= 3⁻¹⁵/⁴ × 3²¹/⁴ × 3²

We know that,

aᵃ × aᵇ = aᵃ⁺ᵇ

= 3⁶/⁴ × 3²

= 3³

= 27

Hence, The answer is 27

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