Question

solve this. I will mark your anwser brainliest ​

Answer 1

Step-by-step explanation:

To prove:

x^a(b-c) / x^b(a-c) ÷ [x^b/x^a]^c = 1

Proof:

$( {x}^{a(b - c)} \div {x}^{b(a - c)} ) \div {( {x}^{b} \div {x}^{a} )}^{c} \\ = ( {x}^{ab - ac} \div {x}^{ba - bc} ) \div ( {x}^{bc} \div {x}^{ac} ) \\ = {(x}^{ab - ac - (ba - bc)} ) \div ( {x}^{(bc - ac)} ) \\ = {x}^{ab - ac - ba + bc - (bc - ac)} \\ = {x}^{(ab \: - \: ac \: - \: ab \: + \: bc \: - \: bc \: + \: ac)} \\ = {x}^{0} \\ = 1$

Points:

• If Base is same, then On Multiplication will make Power to Add.
• If Base is same, then On Division will make Power to Subtract.
• ab = ba || ac = ca || bc = cb
• Any number to the power zero is always one. x^0 = 1

Thanks!