Question

By what number should (7)^6 be multiplied so that the product is (−7)^36?

Answer 1

Let the number be x,

So according to question,

$\sf{ \implies {7}^{6} \times x = ( - 7)^{36} }$

$\sf{ \implies {7}^{6} \times x = ( -1 \times 7)^{36} }$

$\sf{ \implies {7}^{6} \times x = ( -1)^{36} \times 7^{36} }$

$\sf{ \implies{7}^{6} \times x = 1 \times 7^{36} }$

$\sf{ \implies{7}^{6} \times x = 7^{36} }$

$\sf{ \implies x = \frac{ {7}^{36} }{ {7}^{6} } }$

$\sf{ \implies \: x = {7}^{36 - 6} }$

$\pink{ \implies \sf{x = {7}^{30} }}$

Answer 2

Let the number be x,

So according to question,

\sf{ \implies {7}^{6} \times x = ( - 7)^{36} }⟹7

6

×x=(−7)

36

\sf{ \implies {7}^{6} \times x = ( -1 \times 7)^{36} }⟹7

6

×x=(−1×7)

36

\sf{ \implies {7}^{6} \times x = ( -1)^{36} \times 7^{36} }⟹7

6

×x=(−1)

36

×7

36

\sf{ \implies{7}^{6} \times x = 1 \times 7^{36} }⟹7

6

×x=1×7

36

\sf{ \implies{7}^{6} \times x = 7^{36} }⟹7

6

×x=7

36

\begin{gathered} \sf{ \implies x = \frac{ {7}^{36} }{ {7}^{6} } } \\ \end{gathered}

⟹x=

7

6

7

36

\sf{ \implies \: x = {7}^{36 - 6} }⟹x=7

36−6

\pink{ \implies \sf{x = {7}^{30} }}⟹x=7

30