Question

Find the value of k that makes the following expressions a true statement

Answer 1

k=-2 because you need to make the value on the top equal to the value on the bottom for it to be 1, and when multiplying two numbers with the same base you add the exponents, so in this case you would need to add a number to 7 to make it 5, and that number is -2

Hope this helps

Answer 2

`k = - 2`

Explanation:

Since the only variable that is present in this equation is x we can say:

`\frac{ {x}^(7) * {x}^(k) }{ {x}^(5) } = 1 \\ is \: the \: same \: as \\( 7 + k )- 5 = 1 \\ 7 + k = 5 \\`

`k = 5 - 7 \\ k = - 2`

Note that when variables are the same (like in this case where all variables were x) and they are being multiplied, we add the powers, and when the variables are being divided we subtract the powers.