Question

Find the value of k if (-2)k+1× (-2)3= (-2)7

Answer 1

Answer:

4

Step-by-step explanation:

-2)k+1 × (-2)3  = (-2)7​

-2k + -6 = -14

- 2k = -14 + 6

- 2k = - 8

k = -8 / -2

k = 4

Answer 2

To find : value of $k$

Given equation : $(-2) ^{k +1} \times (-2)^{3} = (-2)^{7}$  

Solution :

• As we have to find the value of  $k$, we transpose constant term to RHS leaving variable term at LHS .  
• Given data: $(-2) ^{k +1} \times (-2)^{3} = (-2)^{7}$  

                                      $(-2)^{K + 1} = \frac{(-2)^{7} }{(-2)^{3} }$  

• According to law of indices If the bases of two numbers in the division are the same, then exponents are subtracted and the base will be the same.

          $\frac{x^{a}}{x^{b}}=x^{a-b} .$

• We will apply the above exponents rules, as bases are same ,we get

             $\begin{array}{l}=2^{7-3} \\=2^{4} \\\end{array}$  

• We will apply the above exponents rules, as bases are same ,we get

• Now, equating exponents of LHS and RHS

                         $k + 1 = 4 \\k = 4-1\\k = 3$

Hence , value of $k$ will be $3$.