Question

Escreva (V) ou (F) :
( ) 2 elevado a 7 . 2²= 2 elevado a 9
( ) (7³)² = 7 elevado a 5
( ) 2³ elevado a 2 sobre o 3 =(2³)²
( ) (5.2)² = 5² . 2²
() 10² / 10 elevado a 5= 10 elevado -2

Answer 1

$2^{7} \cdot 2^{2} = 2^{9} \\\\ \boxed{Propriedade \rightarrow x^{a} \cdot x^{b} = x^{a+b}} \\\\ 2^{7+2} = 2^{9} \\\\ 2^{9} = 2^{9} \ \ \boxed{(V)}$


$(7^{3})^{2} = 7^{5} \\\\ \boxed{Propriedade \rightarrow (x^{a})^{b} = x^{a \cdot b}} \\\\ 7^{3 \cdot 2} = 7^{5} \\\\ 7^{6} = 7^{5} \ \ \boxed{(F)}$


$2^{\frac{2}{3}} = (2^{3})^{2} \\\\ 2^{\frac{2}{3}} = 2^{6} \ \ \boxed{(F)}$


$(5 \cdot 2)^{2} = 5^{2} \cdot 2^{2} \\\\ \boxed{Propriedade \rightarrow (x \cdot y)^{a} = x^{a} \cdot y^{a}} \\\\ (10)^{2} = 25 \cdot 4 \\\\ 100 = 100 \ \ \boxed{(V)}$


$\frac{10^{2}}{10^{5}} = 10^{-2} \\\\ \boxed{Propriedade \rightarrow \frac{x^{a}}{x^{b}} = x^{a-b}} \\\\ 10^{2-5} = 10^{-2} \\\\ 10^{-3} = 10^{-2} \ \ \boxed{(F)}$