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defon
2 years ago
5

3⁵.2⁴.2¹.3⁶.(3²)⁴ and down (2³)².3⁶​​

Mathematics
1 answer:
BARSIC [14]2 years ago
4 0

Answer:

\dfrac{3^{13}}{2}

Step-by-step explanation:

Given expression:

\dfrac{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 \dfrac{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 \dfrac{3^{(5+6+8)} \cdot 2^{(4+1)}}{2^6 \cdot 3^6}

\implies \dfrac{3^{19} \cdot 2^{5}}{2^6 \cdot 3^6}

\implies \dfrac{3^{19} \cdot 2^{5}}{3^6 \cdot 2^6}

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

\implies \dfrac{3^{13}}{2^1}

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

\implies \dfrac{3^{13}}{2}

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