Question

who can sole this question is real math lover ​

Answer 1

Recall that:

$y^a \times y^ b = y ^{a + b}$

$y^a \div y^b = y^{a - b}$

Question:

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

First we will attempt to write both the terms in the same number. And here, we can see that  9 can be written as 3²:

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

Now that all the base numbers are 3, we can apply the indices law that states yᵃ x yᵇ = yᵃ⁺ᵇ :

$= \dfrac{3^{n + 2(n + 1)}}{3^{n - 1 + 2(n + 1)}}$

Apply distributive law a(b + c) = ab + ac :

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

Next we will simplify the indices by combine the like terms:

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

Since the base numbers in the numerator and denominator are the same, we can apply the indices law that state  yᵃ ÷ yᵇ = yᵃ⁻ᵇ :

$= 3^{3n + 2 - (3n + 1)}$

$= 3^{3n + 2 - 3n - 1}$

Again, we simplify by combining like terms:

$= 3^{1}$

$= 3$

Answer: 3

Answer 2

Answer:

the answer is 243 .

refer to the attachment for the solution.

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