Question

3⁵.2⁴.2¹.3⁶.(3²)⁴ and down (2³)².3⁶​
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Answer 1

The result is 3¹³ /2

Explanation:

Greetings

Answer 2

`(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)`