Question 1

3⁵.2⁴.2¹.3⁶.(3²)⁴ and down (2³)².3⁶

Question 2

Answer:

The result is 3¹³ /2

Explanation:

Greetings

Question 3

Answer:

(3^(13))/(2)

Explanation:

Given expression:

$(3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot (3^2)^4)/((2^3)^2 \cdot 3^6)$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):$

$\implies (3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot 3^8)/(2^6 \cdot 3^6)$

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

$\implies (3^((5+6+8)) \cdot 2^((4+1)))/(2^6 \cdot 3^6)$

$\implies (3^(19) \cdot 2^(5))/(2^6 \cdot 3^6)$

$\implies (3^(19) \cdot 2^(5))/(3^6 \cdot 2^6)$

$\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):$

$\implies 3^((19-6)) \cdot 2^((5-6))$

$\implies 3^(13) \cdot 2^(-1)$

$\textsf{Apply exponent rule} \quad a^(-n)=(1)/(a^n):$

$\implies (3^(13))/(2^1)$

$\textsf{Apply exponent rule} \quad a^1=a:$

$\implies (3^(13))/(2)$

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