How to Solve with Two Variables in Exponents?

Variable is any value that can be changed according to its requirement or in other words it is indicated as a symbol for any of the number which is unknown. In mathematics, these variables can be represented by small or capital letter as x (or X), y (or Y). Variable in any equation can be made constant by fixing its value. One more thing which is used in mathematics is called an exponent. Exponent can be defined as a power. When we put a power on a variable or a constant then this power will be called as exponent. In other words, we can say that exponent of a constant value or a variable represents the number of times a number is multiplied by itself? Exponents are also called as indices. Let's take an example to understand variable, constant and exponents.

(4x) i. in this example, ‘4’ is a constant, ‘x’ is a variable and ‘i’ is called exponent. Solution will be given by multiplying ‘4x’, ‘i’ times as shown below
4x * 4x * 4x * 4x * 4x……….i times.
Let’s consider that i = 3, then solution will be given as:
(4x) ³ = 4x * 4x * 4x = 64 * 3.
If we take x = 2 then (x)⁴ = (2)⁴ = 2 * 2 * 2 * 2 = 16.
Let’s take an example to understand how to solve with two variables in exponents.
3(y² + 2y + 13) = 27 (-y + 5).
Solution will be derived as shown below:
Since 27 = 33, then above equation can be written as:
3(y² + 2y + 13) = (33) (-y + 5),
Then 3(y² + 2y + 13) = (3) 3(-y + 5),
Since base is same that’s why we can write,
y ² + 2y + 13 = 3 (-y + 5) = - 3y + 15, so
y ² + 2y + 13 + 3y – 15 = 0,
y ² + 5y – 2 = 0.
Above equation can be solved using Quadratic Formula.