Question

7^5 x 7^6= 7^3 x 7^k
find the value of k
please give steps for this answer!

Answer 1

To solve for the value of k in the equation 7^5 x 7^6 = 7^3 x 7^k, we can simplify the exponents and equate them to find k.

Step-by-step explanation:

To solve for the value of k in the equation 7^5 x 7^6 = 7^3 x 7^k, we can use the property of exponents that states when multiplying two expressions with the same base, we add their exponents. So, in this case, we have:

7^(5+6) = 7^(3+k)

Now we can simplify the exponents:

7^11 = 7^(3+k)

Since the bases are the same, we can equate the exponents:

11 = 3 + k

Now we can solve for k by subtracting 3 from both sides:

k = 11 - 3 = 8

Therefore, the value of k is 8.

Answer 2

`7 ^(5 + 6) = 7^(3 + k) \\ 7^(11) = 7 ^(3 + k) \\ (7 ^(11) )/(7 ^(11) ) = (7 ^(3 + k) )/(7 ^(11) ) \\ 1 = 7^(3 + k - 11) \\ 7 ^(0) = 7^( - 8 + k) \\ - 8 + k = 0 \\ k = 8`

HOPE THIS HELPS!!!