Question

3)Aplicando as propriedades da potenciação, escreva cada expressão em uma única potência.
a) (2,5)^10 ÷ (2,5)^2
b) (3/4)^9 × (3/4)^4 × (3/4)
c)(5^6)^7
d)2^5÷2^8​

Answer 1

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$a) \: \: {\green{(2.5) {}^{10} \div (2.5) {}^{2} }} \\ \\ {\green{2.5 {}^{10 - 2} }} \\ \\ {\green{2.5 {}^{8} }} \\ \\ {\green{ \frac{25}{10} }} \\ \\ {\green{ \frac{5}{2} }} \\ \\ {\green{( \frac{5}{2} ) {}^{8} }}$

$b) \: \: {\green{( \frac{3}{4} ) {}^{9} \times ( \frac{3}{4} ) {}^{4} \times ( \frac{3}{4} ) }} \\ \\ {\green{( \frac{3}{4} ) {}^{9} \times ( \frac{3}{4} ) {}^{4} \times ( \frac{3}{4}) {}^{1} }} \\ \\ {\green{( \frac{3}{4} ) {}^{9 + 4 + 1} }} \\ \\ {\green{( \frac{3}{4}) {}^{14} }} \\ \\ {\green{ \frac{3 {}^{14} }{4 {}^{14} } }}$

$c) \: \: {\green{(5 {}^{6}) {}^{7} }} \\ \\{\green{5 {}^{6 \times 7} }} \\ \\ {\green{5 {}^{42} }}$

$d) \: \: {\green{2 {}^{5} \div 2 {}^{8} }} \\ \\ {\green{2 {}^{5 - 8} }} \\ \\ {\green{2 {}^{ - 3} }} \\ \\ {\green{ \frac{1}{2 {}^{3} } }} \\ \\ {\green{ \frac{1}{8} }}$

${\green{Keep \: loving...}}$

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