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jawaban untuk soal nomor 1

Answered by bbita0681 | 2025-08-12

Penyelesaian1. [tex]32^{\frac{4}{5}} \cdot \left(\frac{1}{4}\right)^{-3} \cdot 16^{-\frac{7}{4}}[/tex][tex]32 = 2^5[/tex][tex]32^{\frac{4}{5}} = (2^5)^{\frac{4}{5}} = 2^{5 \cdot \frac{4}{5}}[/tex][tex]= 2^4[/tex][tex]= 16[/tex][tex]\frac{1}{4} = 4^{-1} = (2^2)^{-1}[/tex][tex]\left( \frac{1}{4} \right)^{-3} = \left(2^{-2}\right)^{-3}[/tex][tex]= 2^{6}[/tex][tex]= 64[/tex][tex]16 = 2^4[/tex][tex]16^{-\frac{7}{4}} = (2^4)^{-\frac{7}{4}} = 2^{-7}[/tex][tex]16 \cdot 64 \cdot 2^{-7}[/tex][tex]16 = 2^4[/tex][tex]64 = 2^6[/tex][tex]= 2^4 \cdot 2^6 \cdot 2^{-7}[/tex][tex]= 2^{4+6-7}[/tex][tex]= 2^3[/tex][tex]= 8[/tex]2. [tex](a^2 \cdot b)^3 \cdot (a^2 \cdot b^4)^{-1}[/tex][tex](a^2 \cdot b)^3 = a^{2 \cdot 3} \cdot b^{1 \cdot 3}[/tex][tex]= a^6 \cdot b^3[/tex][tex](a^2 \cdot b^4)^{-1} = a^{2 \cdot (-1)} \cdot b^{4 \cdot (-1)}[/tex][tex]= a^{-2} \cdot b^{-4}[/tex][tex]a^6 \cdot b^3 \cdot a^{-2} \cdot b^{-4} = a^{6-2} \cdot b^{3-4}[/tex][tex]= a^4 \cdot b^{-1}[/tex][tex]a^4 \cdot \frac{1}{b} = \frac{a^4}{b}[/tex]

Answered by vinganzbeut | 2025-08-12