Explicação passo-a-passo:
[tex]a) \frac{512 \div \frac{1}{4} }{ {8}^{2} } = \frac{ {2}^{9} \times 4 }{ {( {2}^{3} )}^{2} } = \frac{ {2}^{9} \times {2}^{2} }{ {2}^{3 \times 2} } = \frac{ {2}^{9 + 2} }{ {2}^{6} } = \\ \\ \frac{ {2}^{11} }{ {2}^{6} } = {2}^{11 - 6} = {2}^{5} [/tex]
[tex]b) \frac{ {4}^{ - 5} \times {8}^{4} }{ {32}^{3} } = \frac{ {( {2}^{2}) }^{ - 5} \times {( {2}^{3} )}^{4} }{ {( {2}^{5}) }^{3} } = \frac{ {2}^{2 \times ( - 5)} \times {2}^{3 \times 4} }{ {2}^{5 \times 3} } = \\ \\ \frac{ {2}^{ - 10} \times {2}^{12} }{ {2}^{15} } = \frac{ {2}^{ - 10 + 12} }{ {2}^{15} } = \frac{ {2}^{2} }{ {2}^{15} } = {2}^{2 - 15} = {2}^{ - 13} [/tex]
[tex]c) \frac{0.25 \times \frac{1}{ {16}^{ - 3} } }{128} = \frac{ \frac{25}{100} \times \frac{1}{ {( {2}^{4} )}^{ - 3} } }{ {2}^{7} } = \frac{ \frac{1}{4} \times \frac{1}{ {2}^{4 \times ( - 3)} } }{ {2}^{7} } = \\ \\ \frac{ \frac{1}{ {2}^{2} } \times \frac{1}{ {2}^{ - 12} } }{ {2}^{7} } = \frac{ {2}^{ - 2} \times {2}^{12} }{ {2}^{7} } = \frac{ {2}^{ - 2 + 12} }{ {2}^{7} } = \\ \\ \frac{ {2}^{10} }{ {2}^{7} } = {2}^{10 - 7} = {2}^{3} [/tex]
Copyright © 2024 ELIBRARY.TIPS - All rights reserved.
Lista de comentários
Explicação passo-a-passo:
[tex]a) \frac{512 \div \frac{1}{4} }{ {8}^{2} } = \frac{ {2}^{9} \times 4 }{ {( {2}^{3} )}^{2} } = \frac{ {2}^{9} \times {2}^{2} }{ {2}^{3 \times 2} } = \frac{ {2}^{9 + 2} }{ {2}^{6} } = \\ \\ \frac{ {2}^{11} }{ {2}^{6} } = {2}^{11 - 6} = {2}^{5} [/tex]
[tex]b) \frac{ {4}^{ - 5} \times {8}^{4} }{ {32}^{3} } = \frac{ {( {2}^{2}) }^{ - 5} \times {( {2}^{3} )}^{4} }{ {( {2}^{5}) }^{3} } = \frac{ {2}^{2 \times ( - 5)} \times {2}^{3 \times 4} }{ {2}^{5 \times 3} } = \\ \\ \frac{ {2}^{ - 10} \times {2}^{12} }{ {2}^{15} } = \frac{ {2}^{ - 10 + 12} }{ {2}^{15} } = \frac{ {2}^{2} }{ {2}^{15} } = {2}^{2 - 15} = {2}^{ - 13} [/tex]
[tex]c) \frac{0.25 \times \frac{1}{ {16}^{ - 3} } }{128} = \frac{ \frac{25}{100} \times \frac{1}{ {( {2}^{4} )}^{ - 3} } }{ {2}^{7} } = \frac{ \frac{1}{4} \times \frac{1}{ {2}^{4 \times ( - 3)} } }{ {2}^{7} } = \\ \\ \frac{ \frac{1}{ {2}^{2} } \times \frac{1}{ {2}^{ - 12} } }{ {2}^{7} } = \frac{ {2}^{ - 2} \times {2}^{12} }{ {2}^{7} } = \frac{ {2}^{ - 2 + 12} }{ {2}^{7} } = \\ \\ \frac{ {2}^{10} }{ {2}^{7} } = {2}^{10 - 7} = {2}^{3} [/tex]