Question

(16a^2)1/2 * (36a^4) * -1/2 / 2a^1/2 * 5a^3/2 * 8a^9/4​

Answer 1

*CORRECT ANSWER

Solve the following;

$\frac{ ( {16a}^{2} )^{ \frac{1}{2} } \times (36a^{4} )^{ - \frac{1}{2} }}{ {2a}^{ \frac{1}{2} } \times {5a}^{ \frac{3}{2} } \times 8a \frac{9}{4} }$

ANSWER

The answer is ;

$\frac{1}{ {120a}^{ \frac{21}{4} } }$

GIVEN

Mathematical expression;

$\frac{ ( {16a}^{2} )^{ \frac{1}{2} } \times (36a^{4} )^{ - \frac{1}{2} }}{ {2a}^{ \frac{1}{2} } \times {5a}^{ \frac{3}{2} } \times 8a^{ \frac{9}{4} } }$

TO FIND

To solve the given expression.

SOLUTION

We can simply solve the above problem as follows;

We know that,

a⁻ⁿ = 1/aⁿ

Therefore,

$= \frac{ ( {16a}^{2} )^{ \frac{1}{2} }}{ {2a}^{ \frac{1}{2} } \times {5a}^{ \frac{3}{2} } \times 8a^{ \frac{9}{4} } \times (36a^{4} )^{ \frac{1}{2} } }$

We know that,

(ab)ⁿ = aⁿ.bⁿ

$= \frac{ ( {16}^{ \frac{1}{2} } \times (a ^{2} )^{ \frac{1}{2} } ) }{2a^{ \frac{1}{2}} \times {5a}^{ \frac{3}{2} } \times {8a}^{ \frac{9}{4} } \times {36}^{ \frac{1}{2} } \times {( {a}^{4} ) }^{ \frac{1}{2} } }$

We can write, 16 as 2⁴ and 36 as 6²

Therefore,

${16}^{ \frac{1}{2} } = (2^{4 \times \frac{1}{2} } ) = 4$

And,

${36}^{ \frac{1}{2} } = ( {6}^{2 \times \frac{1}{2} } ) = 6$

Now,

$= \frac{4a}{2a^{ \frac{1}{2} } \times 5a^{ \frac{3}{2} } \times {2a}^{ \frac{9}{4} } \times 6a²}$

Crossing out the common factor in fraction;

$= \frac{1}{2a^{ \frac{1}{2} } \times 5a^{ \frac{3}{2} } \times 2a^{ \frac{9}{4} } \times 6a }$

Multiplying the monomials

$= \frac{1}{120a^{ \frac{21}{4} } }$

Hence, The answer is;

$\frac{1}{ {120a}^{ \frac{21}{4} } }$

#SPJ1

Answer 2

Explanation:

*CORRECT ANSWER

Solve the following;

\frac{ ( {16a}^{2} )^{ \frac{1}{2} } \times (36a^{4} )^{ - \frac{1}{2} }}{ {2a}^{ \frac{1}{2} } \times {5a}^{ \frac{3}{2} } \times 8a \frac{9}{4} }2a21×5a23×8a49(16a2)21×(36a4)−21

ANSWER

The answer is ;

\frac{1}{ {120a}^{ \frac{21}{4} } }120a4211

GIVEN

Mathematical expression;

\frac{ ( {16a}^{2} )^{ \frac{1}{2} } \times (36a^{4} )^{ - \frac{1}{2} }}{ {2a}^{ \frac{1}{2} } \times {5a}^{ \frac{3}{2} } \times 8a^{ \frac{9}{4} } }2a21×5a23×8a49(16a2)21×(36a4)−21

TO FIND

To solve the given expression.

SOLUTION

We can simply solve the above problem as follows;

We know that,

a⁻ⁿ = 1/aⁿ

Therefore,

= \frac{ ( {16a}^{2} )^{ \frac{1}{2} }}{ {2a}^{ \frac{1}{2} } \times {5a}^{ \frac{3}{2} } \times 8a^{ \frac{9}{4} } \times (36a^{4} )^{ \frac{1}{2} } }=2a21×5a23×8a49×(36a4)21(16a2)21

We know that,

(ab)ⁿ = aⁿ.bⁿ

= \frac{ ( {16}^{ \frac{1}{2} } \times (a ^{2} )^{ \frac{1}{2} } ) }{2a^{ \frac{1}{2}} \times {5a}^{ \frac{3}{2} } \times {8a}^{ \frac{9}{4} } \times {36}^{ \frac{1}{2} } \times {( {a}^{4} ) }^{ \frac{1}{2} } }=2a21×5a23×8a49×3621×(a4)21(1621×(a2)21)

We can write, 16 as 2⁴ and 36 as 6²

Therefore,

{16}^{ \frac{1}{2} } = (2^{4 \times \frac{1}{2} } ) = 41621=(24×21)=4

And,

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