Question

cube root of 3^6×4^3×2^9/8^6×2^6

Answer 1

Answer:

9/8 by teacher answer

3 6 1/3*4 3 1/3 * 2 6 1/3 / (8 6 1/3 *2 )6 1/3 cancellation 9*4*8/64*4 44 two fours will get cancelled 8*8=64 so 64 will get 8 answer is 9/8 if you didn't understand then you write simply multiplication and answer

Answer 2

Given,

An expression: 3^6×4^3×2^9/8^6×2^6

To find,

The cube root of the given expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

For any variables x, a, and b,

{(x)^a}^b = (x)^(a×b)

{Statement-1}

The cube root of the given expression can be calculated as follows:

(3^6×4^3×2^9/8^6×2^6)^1/3

= {(3^6)^1/3 × (4^3)^1/3 × (2^9)^1/3} ÷ {(8^6)^1/3 × (2^6)^1/3}

= {(3)^6×1/3 × (4)^3×1/3 × (2)^9×1/3} ÷ {(8)^6×1/3 × (2)^6×1/3}

(according to statement-1)

= {(3)^2 × (4)^1 × (2)^3} ÷ {(8)^2 × (2)^2}

= {9 × 4 × 8} ÷ {8 × 8 × 4}

= 9/8

Hence, the cube root of the given expression is equal to 9/8.