Question

Guys pls help. Pls give me correct answer.​

Answer 1

Answer:

(91)³

Step-by-step explanation:

Given Question:

Simplify:

$\bf{\dfrac{3^2 \times 7^8 \times 13^6}{21^2 \times 91^3}}$

Solution:

As we can observe there are bigger numbers in the denominator.

So let us apply laws of exponents to simplify the denominator.

Laws of exponents used:

• aᵐ × aⁿ = aᵐ⁺ⁿ
• (a × b)ᵐ = aᵐ × bᵐ

Now, 21 can be written as (7 × 3) and 91 can be written as (13 × 7)

Now the expression becomes:

$\dashrightarrow \: \: \: \sf{\dfrac{3^2 \times 7^8 \times 13^6}{(3 \times 7)^{2}\times(13 \times 7)^{3}}}$

Using identity (a × b)ᵐ = aᵐ × bᵐ in denominator,

$\Rightarrow \: \sf{\dfrac{3^2 \times 7^8 \times 13^6}{7^2 \times 3^2 \times 13^3 \times 7^3}}$

Cancel 3² in both numerator and denominator

$\Rightarrow \: \sf{\dfrac{\not{3^2} \times 7^8 \times 13^6}{7^2 \times \not{3^2} \times 13^3 \times 7^3}}$

$\Rightarrow \: \sf{\dfrac{7^8 \times 13^6}{7^2 \times 13^3 \times 7^3}}$

Apply identity aᵐ × aⁿ = aᵐ⁺ⁿ

$\Rightarrow \: \sf{\dfrac{7^8 \times 13^6}{13^3 \times 7^{(3+2)}}}$

$\Rightarrow \: \sf{\dfrac{7^8 \times 13^6}{13^3 \times 7^{5}}}$

On grouping,

$\Rightarrow \: \sf{\dfrac{7^8}{7^5}\times \dfrac{13^6}{13^3}}$

Using identity aᵐ ÷ aⁿ = aᵐ⁻ⁿ

$\Rightarrow \: \sf{7^{(8-5)}\times 13^{(6-3)}}$

$\Rightarrow \: \sf{7^3 \times 13^3}$

Applying the converse of identity aᵐ × bᵐ = (a × b)ᵐ

So,

$\longrightarrow \: \sf{(7 \times 13)^3}$

$= \sf{(91)^3}$

$\therefore \boxed{ \boldsymbol{\dfrac{3^2 \times 7^8 \times 13^6}{21^2 \times 91^3}=(91)^3}}$

Answer 2

Step-by-step explanation:

$\frac{ {3}^{2} \times {7}^{8} \times {13}^{6} }{ {21}^{2} \times {91}^{3} } \\ = \frac{ {3}^{2} \times {7}^{8} \times {13}^{6} }{ {(3 \times 7)}^{2} \times {(13 \times 7)}^{3} } \\ = \frac{ \cancel{3}^{2} \times {7}^{8} \times {13}^{6} }{ \cancel{{3}^{2}} \times {7}^{2} \times {13}^{3} \times {7}^{3} } \\ = \frac{ {7}^{8} \times {13}^{6} }{ {7}^{2 + 3} \times {13}^{3} } \\ = \frac{ {7}^{8 } \times {13}^{6} }{ {7}^{5} \times {13}^{3} } \\ = {7}^{8 - 5} \times {13}^{6 - 3} \\ = {7}^{3} \times {13}^{3} \\ = {91}^{3}$