Question

the answer to this equation is negative 6 but I don’t know to explain how I got the answer is word form.

Answer 1

The value of k is –6.

Solution:

Given equation:

`$(5 \cdot 5^(k))/(5^(-8))=5^(3)`

To find the value of k:

`$(5 \cdot 5^(k))/(5^(-8))=5^(3)`

Using exponent rule:
`a^m \cdot a^n = a^(m+n)`

`$(5^(1+k))/(5^(-8))=5^(3)`

Using exponent rule:
`(1)/(a^(-m)) = a^(m)`

`$ 5^(1+k) \cdot 5^(8)=5^(3)`

Using exponent rule:
`a^m \cdot a^n = a^(m+n)`

`$ 5^(1+k+8)=5^(3)`

`$ 5^(k+9)=5^(3)`

If the bases are same then, we can equate the powers of the bases.

i. e. If
`a^m = a^n` then m = n.

k + 9 = 3

Subtract 9 from both sides of the equation, we get

k = –6

Hence the value of k is –6.