Question

solve this indices or( power and exponent) math ​

Answer 1

Answer:

3

Rules used:

• $\\\tt ( x^{b})^{a} = x^{ab}$

• $\\\tt x^{a} * x^{b} = x^{a+b}$

• $\\\tt \dfrac{x^{a}}{x^{b}} = x^{a-b}$

Step-by-step explanation:

$\dfrac{ {3}^{n} \times {9}^{n + 1} } { {3}^{n - 1} \times {9}^{n - 1} } \\ = \dfrac{ {3}^{n} \times {3}^{2n + 2} } { {3}^{n - 1} \times {3}^{2n - 2} } \\ = \dfrac{ {3}^{n + 2n+ 2} } { {3}^{n - 1 + 2n + 2} } \\ = \dfrac{ {3}^{3n+ 2} } { {3}^{3n + 1} } \\ = {3}^{3n + 2 - 3n - 1} \\ = {3}^{1} = 3$