What is the value of y^12 * z^-4 if y^6 = z^2 = 5?
Advanced Placement (AP) · Middle School · Sun Jan 24 2021
Answered on
To solve for the value of y^12 * z^-4 given that y^6 = z^2 = 5, we can break this problem into smaller parts:
1. Given that y^6 = 5, we can find y^12 by squaring both sides. So:
(y^6)^2 = 5^2 y^(6*2) = 25 y^12 = 25
2. Similarly, given that z^2 = 5, to find z^-4 we first need to find z^4 and then take its reciprocal since a negative exponent represents the reciprocal of the base raised to the positive exponent:
(z^2)^2 = 5^2 z^4 = 25
Now for z^-4, we take the reciprocal of z^4: z^-4 = 1/z^4 z^-4 = 1/25
3. We can now combine these results to find the value of y^12 * z^-4:
y^12 * z^-4 = 25 * (1/25)
4. When you multiply 25 by 1/25, the result is:
25 * 1/25 = 25/25 25/25 = 1 (since any number divided by itself equals 1)
So, the value of y^12 * z^-4 is 1.