Question

27^6 divided by 9^5. Write in simplest index form. Thx.

Answer 1

3⁸

Explanation:

27 = 3* 3 * 3 = 3³

9 = 3 * 3 = 3²

Write 27 and 9 with base 3.

Law of exponents:

`\boxed{(a^m)^n=a^(m*n) \ and \ (a^m)/(a^n)=a^(m-n)}`

In exponent division, if bases are same, subtract the exponents/index.

`(27^6)/(9^5)=((3^3)^6)/((3^2)^5)`

`=(3^(3*6))/(3^(2*5))\\\\\\=(3^(18))/(3^(10))\\\\\\=3^(18-10)\\\\=3^(8)`