Q&A for How to Add Exponents

Since the two expressions have the same base (x) and the same variable (3), you can just add the coefficients. If a variable has no coefficient, it really has a coefficient of 1. The exponents will stay the same. So: x^3 + x^3 (1)x^3 + (1)x^3 2x^3

The exponents are not same, therefore it is impossible to add it.

X^2 +X^-2. It cancels itself because ^2 and ^-2 are opposites. That makes X raised to the 1st. X^1 is X.

An exponent affects only its base and nothing else. Therefore, it wouldn't make sense to add (or subtract) exponents of different bases.

It's simple addition. An example: x^2 multiplied by x^4 equals x^(2+4), or x^6.

First, x + x is 2x. When you raise 2x to the third power, you get 8x^3.

x² + x² + 4x = 2x² + 4x = 2x(x + 2).

13² + 15² = 169 + 225 = 394.

Remember BODMAS (Brackets of division, multiplication, addition and subtraction) meaning you always divide or multiply before doing addition or subtraction. Then you need to get X alone. Remember also that when taking figures to the other side of the equal sign, you need to change it either from a positive to a negative or vice versa, depending on what it originally was. 4X + 14 - 44 = ? 4X = 44 - 14 4X = 30 X = 30/4 X=7.5

Discover what the variable is, then multiply it by itself the number of time sthe exponemt tells you. For example: 4 3, x + x =. If x=5, 5x 5 x 5 x 5 = 625, 5 x 5 x 5 = 125, 125 + 625 = 750.

The left side of the equation consists of four groups of 4^44. That can be re-written as 4 x 4^44 (or 4^1 x 4^44, which equals 4^45). That means 4^45 = 4^x. Therefore, x = 45.

You can solve this by inspection: you want to add some power of 9 to some power of 3 in order to get 36. We know that 27 + 9 = 36. 9^(3/2) = 27, and 3² = 9. So we need (x+1) to equal 3/2, and it does if x=½. We need (2x+1) to equal 2, and it does if x = ½. So the equation works when x=½.

Yes, if you define x² + 4x as "impossible," 2x² + 4x would be similarly "impossible."

√5x = (√5)(√x), and √7x = (√7)(√x). So the above expression can be written [(√5)(√x) + (√7)(√x)], which equals [(√5 + √7)(√x)] = (2.236 + 2.646)(√x) = 4.882√x.

If you take the natural log on both sides, you're allowed to say that x ln 8 = 2x ln 6. We notice that if we cancel x, we get the contradiction ln 8 = 2ln 6, which is impossible. However, note that x can be zero, and satisfies 8^x=6^2x=1.

No. It's just simply x² + x³. That can be factored into x²(1 + x), but that doesn't combine the two terms in any way.

First of all, the bases have to be the same before the numbers can be added together. (In your example, the bases are not the same.) Also, when exponents contain variables (as in your example), the numbers cannot be numerically evaluated in order to add them together.

This simplifies to 2(3^3x) + 3 = 108. 2(3^3x) = 105, 3^3x = 105/2, 3x = log3(105/2), x = log3(105/2)/3. Using the relationship log3(x) = log10(x)/log10(3), we can calculate log3(105/2)/3 to log10(105/2)/log10(3) x 1/3 ~= 1.202