Question

simplify
$( - 4) {}^{5} \times ( - 4) {}^{ - 10}$
and
$(2) {}^{5} \div (2) {}^{ - 6}$
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Answer 1

ANSWER :

1) -4^(5) × -4^(-10)

(By using property a^x × a^y = a^x+y)

= -4^[5+(-10)]

= -4^(5-10)

= -4^(-5)

2) 2^(5)/2^(-6)

(By using property a^x/a^y = a^x-y)

= 2^[5-(-6)]

= 2^11

Answer 2

Answer:

$(1) \: ( - 4) {}^{5} \times ( - 4) {}^{ - 10} = ( - 4) {}^{5 - 10} \\ = \frac{1}{( - 4) {}^{5} } \\ = (a {}^{m} \times a {}^{n}) = a {}^{m + n..} a {}^{ - m} = \frac{1}{a {}^{m} } \\ (2) \: (2 {}^{5} \div 2 {}^{ - 6} ) = 2 {}^{5 - ( - 6)} = 2 {}^{11} \\ = (a {}^{m} \div a {}^{n} ) \\ = (a {}^{m} - n )$