Question

4×81^-1/2(81^1/2+81^3/2)

Answer 1

Answer:

328

Step-by-step explanation:

Assume that the given expression is

$4\times 81^{-\frac{1}{2}}\times (81^{\frac{1}{2}}+81^{\frac{3}{2}})$

Using the power property of exponent.

$4\times (81^{\frac{1}{2}})^{-1}\times (81^{\frac{1}{2}}+(81^{\frac{1}{2}})^3)$                          $[\because a^{mn}=(a^m)^n]$

$4\times (9)^{-1}\times (9+(9)^3)$

On further simplification.

$4\times (9)^{-1}\times (9+729)$

$4\times (9)^{-1}\times 738$

Using the negative power property of exponent.

$4\times \frac{1}{9}\times 738$                     $[\because a^{-n}=\frac{1}{a^n}]$

Cancel out the common factors.

$4\times 82$

$328$

Therefore, the value of given expression is 328.

Answer 2

Answer:

Answer:

328

Step-by-step explanation:

Assume that the given expression is

4\times 81^{-\frac{1}{2}}\times (81^{\frac{1}{2}}+81^{\frac{3}{2}})4×81

−

2

1

×(81

2

1

+81

2

3

)

Using the power property of exponent.

4\times (81^{\frac{1}{2}})^{-1}\times (81^{\frac{1}{2}}+(81^{\frac{1}{2}})^3)4×(81

2

1

)

−1

×(81

2

1

+(81

2

1

)

3

) [\because a^{mn}=(a^m)^n][∵a

mn

=(a

m

)

n

]

4\times (9)^{-1}\times (9+(9)^3)4×(9)

−1

×(9+(9)

3

)

On further simplification.

4\times (9)^{-1}\times (9+729)4×(9)

−1

×(9+729)

4\times (9)^{-1}\times 7384×(9)

−1

×738

Using the negative power property of exponent.

4\times \frac{1}{9}\times 7384×

9

1

×738 [\because a^{-n}=\frac{1}{a^n}][∵a

−n

=

a

n

1

]

Cancel out the common factors.

4\times 824×82

328328

Therefore, the value of given expression is 328.