To find the missing exponent, let's simplify both sides of the equation:
On the left side, we have k^5 * k^2 / k^x.
When dividing with the same base, we subtract the exponents, so this simplifies to k^(5+2-x) = k^(7-x).
On the right side, we have (k^2)^-2.
When raising a power to another power, we multiply the exponents, so this simplifies to k^(2*-2) = k^(-4).
Now, we can set the two expressions equal to each other and solve for x:
k^(7-x) = k^(-4)
Since the bases are the same, the exponents must be equal:
7 - x = -4
To isolate x, we can add x to both sides:
7 - x + x = -4 + x
7 = -4 + x
To further isolate x, we can subtract -4 from both sides:
7 + 4 = -4 + x + 4
11 = x
Therefore, the missing exponent x that would make the equation true is x = 11.
what is the missing exponent that would make this equation true
k^5 ∙ k^2/k^x = (k^2)^-2
1 answer
3 answers