Question

use the laws of exponents and simplify

Answer 1

There are 8 laws of exponent.
1 law : For any rational number p/q and any integer m.( P/q)m=p*m/p*q.
2 law:For any rational number p/qand positive integers m and n. (P/q)m*(p/q)n=(p/q)m+n.
3 law : for any rational number p/q and positive integers m and n. (P/q)m ➗ (p/q)n=(p/q)m-n.
Law 4: For any non-zero rational number p/q and positive integer K, (p/q)-k=(q/p)k. (P/q)-k=(p/q)-1*k={(p/q)-1}ka=(q/p)k
Law 6:for any non-zero rational number p/q.
Law 7: For any two rational numbers p/q and a/b,and a positive integer m.
Law 8:For any two rational numbers p/q and a/b, and a positive integer m.

Answer 2

Answer:

The value of  using laws of exponents 12⁶/162 = 2¹¹*3²

Step-by-step explanation:

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = xᵃᵇ

xᵃ/xᵇ = xᵃ⁻ᵇ

It is given that,

(12)⁶/162

Find the value of (12)⁶/162

By using laws of exponents we can write,

(12)⁶/162 = (3*4)⁶/(2*81)

  = (3*2²)⁶/(2*3⁴)

  = (3⁶*2¹²)/(2*3⁴)

  = (2¹²*3⁶)/(2*3⁴)

  = 2¹²⁻¹*3⁶⁻⁴

  = 2¹¹*3²

Therefore the value of  using laws of exponents 12⁶/162 = 2¹¹*3²