Question

find the value with all steps​

Answer 1

Answer:

Cube root of (-343) = -7

Cube root of (-1331) = -11

= (-7)×(-11)

= 77

Answer 2

Required Solution :-

$\sf :\implies^3\sqrt{(-343)\times (-1331)}$

Write the interior terms of under-root in its prime factors.

$\sf :\implies^3\sqrt{({\bf {-1}}\times 7 \times 7\times 7)\times ({\bf{-1}}\times 11\times 11\times 11)}$

Here -1×-1 will become 1, then:

$\sf :\implies^3\sqrt{( 7 \times 7\times 7)\times ( 11\times 11\times 11)}$

Now making triplets:

$\sf :\implies^3\sqrt{( 7 \times 11)\times (7\times11)\times (7\times 11)}$

Now removing cube root and add ⅓ as exponent:

$\sf :\implies\Big[( 7 \times 11)\times (7\times11)\times (7\times 11)\Big]^\dfrac{1}{3}$

Now express inner terms of bracket in exponential form:

$\sf :\implies\Big[( 7 \times 11)^3\Big]^\dfrac{1}{3}$

Applying exponential rule:-

• (Aᵃ)ᵇ=Aᵃᵇ

So,

$\sf :\implies\Big( 7 \times 11\Big)^\dfrac{1}{\bf 3}\times \Large {\bf 3}$

$\sf :\implies\Big( 7 \times 11\Big)^\dfrac{1}{\not 3}\times \Large {\not 3}$

$\sf :\implies\Big(\bf 7 \times 11\Big)$

$\sf\boxed{ :\implies 77}$

So the required answer is 77.