Question

[(243)n/5×(3)2n+1]/9n×3n-1=?

Answer 1

Given Expression
=     (243)(n/5) x 32n + 19n x 3n – 1=     (35)(n/5) x 32n + 1(32)n x 3n – 1=     (35 x (n/5) x 32n + 1)(32n x 3n – 1)=     3n x 32n + 132n x 3n – 1=     3(n + 2n + 1)3(2n + n – 1)=33n + 133n – 1= 3(3n + 1 – 3n + 1)   = 32   = 9.12.1     +     1     = ?
1 + a(n – m)     1 + a(m – n)
A.     0    B.
1
2
C.     1    D.     am + n
Answer & ExplanationAnswer: Option CExplanation:1     +     1     =
1      +      1
1 +     an
am1 +     am
an
1 + a(n – m)     1 + a(m – n)=     am     +     an
(am + an)     (am + an)=     (am + an)
(am + an)= 1.13.

Answer 2

The value of given expression is 9.

Step-by-step explanation:

Consider the given expression is

$\dfrac{(243)^{n/5}\times 3^{2n+1}}{9^n\times 3^{n-1}}$

We need to find the simplified form of given expression.

The given expression can be rewritten as

$\dfrac{(3^5)^{n/5}\times 3^{2n+1}}{(3^2)^n\times 3^{n-1}}$

Using the properties of exponents we get

$\dfrac{3^n\times 3^{2n+1}}{3^{2n}\times 3^{n-1}}$                      $[\because (a^m)^n=a^{mn}]$

$\dfrac{3^{n+2n+1}}{3^{2n+n-1}}$                      $[\because a^ma^n=a^{m+n}]$

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

$3^{3n+1-3n+1}$                 $[\because \dfrac{a^m}{a^n}=a^{m-n}]$

$3^2$

$9$

Therefore, the value of given expression is 9.

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