Question

(A^5)^6 × a^2 × (a^8)^0

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

Answer 1

Answer:

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

Step-by-step explanation:

Given:

(a^5)^6 × a^2 × (a^8)^0

Solution:

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

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

Therefore the required equation will be

(a^5)^6 × a^2 × (a^8)^0  

$(a^{5}) ^{6}\times a^{2}\times (a^{8})^{0} =a^{(30)}\times a^{2}\times a^{0}$

2. law of indices

$x^{a} \times x^{b} = x^{(a+b)}$

Therefore,

$(a^{5}) ^{6}\times a^{2}\times (a^{8})^{0} = a^{(30+2+0)}$

$(a^{5}) ^{6}\times a^{2}\times (a^{8})^{0} = a^{(32)}$