Final answer:
To find the value of each variable that makes the equation true, we can follow the steps outlined below.
Step-by-step explanation:
To find the value of each variable that makes the equation true:
a) To solve 2d⁴ = 2¹², divide both sides by 2: d⁴ = 2¹¹. Take the fourth root of both sides to isolate d: d = (√2¹¹)⁴ = 2³ = 8.
b) To solve 3⁵ x 7⁵ = e⁵, we can rewrite it as (3 x 7)⁵ = e⁵. This means e must be equal to 3 x 7 = 21.
c) To solve 5⁰ x 5ᶠ = 5⁴, anything raised to the power of zero is equal to 1, so we have 1 x 5ᶠ = 5⁴. To isolate f, we can divide both sides by 1: 5ᶠ = 5⁴. Since the bases are the same, we can equate the exponents: f = 4.