Question

Aplicamos propiedades de la potenciación.
a) (−2)4 + (−2)5 =

b)(5)$^{3}$ − 5$^{0}$ =

c)$\frac{21^{6}.35^{3} }{15x^{3}.7^{6} }=$

d)$(\frac{1}{5}^{8})\\(\frac{1}{5}^{5})$

e)$(\frac{1}{2}^{-2}).2^{3}$

f)((−2)3)2 + (−2)2 =

Answer 1

${( - 2)}^{4} + {( - 2)}^{5} = 16 - 32 = - 16$

${5}^{3} - {5}^{0} = 125 - 1 = 124$

$\frac{{21}^{6} \times {35}^{3} }{15 {x}^{3} \times {7}^{6} } = \frac{ {3}^{6} \times {7}^{6} \times {7}^{3} \times {5}^{3} }{ 3 \times 5 \times {x}^{3} \times {7}^{6} } = \frac{ {3}^{5} \times {7}^{3} \times {5}^{2} }{ {x}^{3} } \\ \frac{ {(3 \times 7 \times 5)}^{2} \times {3}^{3} \times 7 }{ {x}^{3} } = \frac{ {105}^{2} \times {3}^{3} \times 7}{ {x}^{3} }$

${( \frac{1}{5}) }^{8} \div { (\frac{1}{5} )}^{5} = { (\frac{1}{5} )}^{8 - 5} = {( \frac{1}{5} )}^{3} = \frac{1}{125} = {125}^{ - 1}$

${(\frac{1}{2}) }^{ - 2} \times {2}^{3} = { (\frac{2}{1} )}^{ - ( - 2)} \times {2}^{3} = {2}^{2} \times {2}^{3} \\ {2}^{2 + 3} = {2}^{5} = 32$

${( {( - 2)}^{3} )}^{2} + {( - 2)}^{2} = {( - 2)}^{3 \times 2} + 4 = { ( - 2)}^{6} + 4 \\ 64 + 4 = 68$