Question

scrieti sub foma de putere 4 la puterea 2 imultit cu 8  la puterea 3 imultit cu 2 la puterea 5 imultit cu 16
47 imultit cu47 la puterea 2 imultit cu 47 la puterea 5
CALCULATI
14 LA PUTERE 2-10 LA PUTEREA 2-8 LA PUTEREA 2
2 LA PUTEREA 5-2 LA PUTEREA 3-9 LA PUTEREA 0
7 LA PUTEREA 3-14 LA PUTEREA 2-7 LA PUTEREA 1

Answer 1

1.  4^{2} x 8^{3} x 2^{5} x 16= (2² )^{2} x (2³ )^{3} x 2^{5} x 2^{4}=
= 2^{2x2} x 2^{3x3}x 2^{5} x 2^{4} = 2^{4} x 2^{9} x 2^{5} x 2^{4}=
= 2^{4+9+5+4} =2^{22}

2. 47 x 47^{2} x 47^{5} = 47^{1+2+5} = 47^{8}

3. 14^{2} - 10^{2} -8^{2} =(2 x 7)^{2} - (2 x 5)^{2} -(2 x 4)^{2} =
=2^{2} x (7^{2} - 5^{2} - 4^{2} ) = 4 x (49-25-16)=4 x 8 =32

4. 2^{5} - 2^{3} - 9^{0} = 2^{3+2} - 2^{3} - 1 = 2^{3} x (2^{2} - 1) - 1=
=8 x (4-1) - 1=8 x 3 -1=23
 
5. 7^{3} - 14^{2} - 7^{1} = 7^{3} - (2 x 7 )^{2} - 7^{1} =
=7^{1} x (7^{3-1} - 7^{1} x 2^{2} -1) = 7 x (7^{2} - 7 x 4 -1)=
=7 x (49-28-1)=7 x 20=140