i would like to compare two quantity,first is
$-3^4$ and $(-3)^4$,second one is clearly $81$,but what about second on?is it $-3\cdot-3\cdot-3\cdot-3$ ? $-3\cdot3\cdot3\cdot3$?there could be such kind of question on GRE exam and i should know answer on this question,please help me
Note that exponents have higher precedence than the unary operation of negation, so: $$ -3^4=-(3^4)=-(3 \cdot 3 \cdot 3 \cdot 3)=-(81)=-81 $$ while on the other hand: $$ (-3)^4=(-3) \cdot (-3) \cdot (-3) \cdot (-3)=81 $$
If you've heard of the mnemonic device BEDMAS, you can think of the unary operation of a negation such as $-x$ as really being the binary operation of the subtraction $0-x$. Hence, since "E" comes before "S", we apply the exponent first before the negative sign (that is, before subtracting it from $0$).