Question

what is the simplified expression​

Answer 1

Solution:

$\rightarrow \frac{4^{-3} \times 3^{4} \times 4^{2} }{3^{5} \times 4^{-2} }$

$\rightarrow 4^{-3 + 2} \times 3^{4 - 5} \times 4^{2} }$

$\rightarrow 4^{-1} \times 3^{-1} \times 16}$

$\rightarrow \frac{1}{4} \times \frac{1}{3} \times 16}$

$\rightarrow \frac{1}{12} \times 16}$

$\rightarrow \frac{16}{12}$

$\rightarrow \boxed{\bold{\frac{4}{3} \tex\text{ (Option B)}}}$

Answer 2

Answer:

$\dfrac43$

Step-by-step explanation:

      $\dfrac{4^{-3}\cdot3^4\cdot4^2}{3^5\cdot4^{-2}}$

Separate like terms:

$\implies \dfrac{4^{-3}\cdot4^2}{4^{-2}}\cdot \dfrac{3^4}{3^5}$

Use exponent rule $a^b \cdot a^c=a^{(b+c)}$ :

$\implies \dfrac{4^{(-3+2)}}{4^{-2}}\cdot \dfrac{3^4}{3^5}$

$\implies \dfrac{4^{-1}}{4^{-2}}\cdot \dfrac{3^4}{3^5}$

Use exponent rule   $\dfrac{a^b}{a^c}=a^{(b-c)}$

$\implies 4^{(-1--2)}\cdot {3^{(4-5)}$

$\implies 4^{1}\cdot {3^{-1}$

Use exponent rule  $a^{-1}=\dfrac{1}{a}$

$\implies 4\cdot \dfrac13$

$\implies \dfrac43$