Question

(A^5)^6 × a^2 × (a^8)^0

Could you show me the steps so I can understand better?

Answer 1

The answer for (a^5)^6 × a^2 × (a^8)^0 is a^32 or
`a^(32)`

Explanation:

Given:

(a^5)^6 × a^2 × (a^8)^0

Solution:

1.By property of indices or law of indices we have

`(x^(a)) ^(b) = x^((a* b))\\ \therefore (a^(5)) ^(6) = a^((5* 6))\\ \therefore (a^(5)) ^(6) = a^((30))\\Similarly\\a^(2) = a^(2)\\ \\(a^(8))^(0)} = a^((8* 0))\\(a^(8))^(0)} = a^(0)\ \textrm{Which is also equal to one i.e 1}\\`

Therefore the required equation will be

(a^5)^6 × a^2 × (a^8)^0

`(a^(5)) ^(6)* a^(2)* (a^(8))^(0) =a^((30))* a^(2)* a^(0)`

2. law of indices

`x^(a) * x^(b) = x^((a+b))\\`

Therefore,

`(a^(5)) ^(6)* a^(2)* (a^(8))^(0) = a^((30+2+0))`

`(a^(5)) ^(6)* a^(2)* (a^(8))^(0) = a^((32))`