Question

-7×-7×-7×-7 in exponential form​

Answer 1

Answer:

7^4

(-7)^4=(-1)^4×(7)^4

-1 raised to even number is 1

so 1× 7^4=7^4

Answer 2

$\huge\mathbb\color{purple}{AN}\purple{SW}\pink{ER}\color{pink}{:}$

Method - 1:

$( - 7) \times ( - 7) \times ( - 7) \times ( - 7) \\ = ( - 1) \times ( -1 ) \times 7 \times 7 \times ( - 7) \times ( - 7) \\ = 1 \times 7 \times 7 \times ( -1 ) \times ( -1 ) \times 7 \times 7 \\ = 7 \times 7 \times 1\times 7 \times 7 \\ = {7}^{4}$

Note :

$( - ) \times ( - ) = ( + ) \\ ( - ) \times ( + ) = ( - )$

Method -2 :

$( - 7) \times ( - 7) \times ( - 7) \times ( - 7) \\ = ( -1 ) \times ( -1 ) \times ( - 1) \times ( - 1) \times 7 \times 7 \times 7 \times 7 \\ = {( - 1)}^{4} \times {7}^{4} \\ = 1 \times {7}^{4} \\ = {7}^{4}$

Note :

${( - 1)}^{n} \\ = 1 \: \: \: when \: \: \: n \: = even \\ = - 1 \: \: \: when \: \: \: n \: = \: odd$