Q&A for How to Solve Exponents

A denominator in an exponent is the same thing as a root. For example, a square root is the same thing as x^(1/2).

When you have negative exponents, you're taking the reciprocal of whatever the base is. For example, x^-2 would be the same as 1/(x^2).

If you're multiplying exponents that have the same base, add the exponents together. So if you have x^2 times x^3, it becomes x^5. But if you're taking the exponent of a base that already has an exponent, you multiply those exponents together. For instance, if you're finding (x^2)^3, you'd multiply the 2 and the 3 to get x^6.

Looking at the exponent 2/3, the 2 is a normal exponent (meaning you square the base number). The 3 is a root sign (meaning you find the cube root). In this case you would square 3 -- which is 9 -- and then you find the cube root of 9. If you wanted to, you could reverse the order of those two operations by first finding the cube root of 3 and then squaring that number. In either case the answer would be the same.

Four to the power of 2 is 16, since 4 times 4 is 16. Then you divide by 3, so 16 divided by 3 is 16/3.

I assume you mean 2^(3/2). Anything to the first power is itself so 2^1 is just 2. Half exponents are square roots, so 2^(1/2) = √2. (Why? because of the same rule: (2^(½))×(2^(½)) = 2^(½ +½) = 2^1 = 2. Also, √2×√2 = 2). We can write out 2^(3/2) = 2^(½+½+½ ) = 2^(½)×2^(½)×2^(½) or √2×√2×√2 = 2^1×2^(½) = 2×√2. So the product simplifies to 2×sqrt(2) or 2√2.

√125 can be thought of as 125 raised to the power of ½ (or 125^½). 125^½ raised to the sixth power is 125^3 = 1,953,125.

(x^0.4)/16 = 32/(x^2.6). By cross multiplication, x^3 =16*32 =2^(4+5) [Exponents] =2^9. So, x = 2^3 =8.

You cube root (3a)^3, so the exponent 3 can be cancelled out by the cube root, and all you have now is 3a.

The Richter scale is a log 10 scale. This means that when you calculate ratios, you calculate them using your numbers in the exponents, and 10 is in the base. For example, 10^5/10^4 = 10. So 10^5.5/10^4 = 31.62 - it's 31.62x stronger.

10^1,3= 10^4/3; that means that the bottom number is the exponent of a root of the number to the upper number, i.e., ∛(10^4) in this specific situation.

Negative exponents indicate reciprocals. If you have 8^-5, that would be ⅛^5. If you have ⅛^-5, that will be 8^5.

One of the easiest ways to do this is to make sure you're working with one type of unit. You need to convert all the units and cancel out the units where applicable. For example, if you are given minutes for one part of the equation and hours for another, you should convert one of those into the other (1 hour equals 60 mins). Then do the math and convert back if you need to.

You would need a calculator that does roots, because the exponent 1/6 means the sixth root of the base number. The sixth root is the cube root of the square root.

The best way to solve this is by inspection, which means to look carefully at the question, and figure it out logically. Notice that you're dealing with a fraction that has to become an integer. You can accomplish this by applying a negative exponent. Thus, x will be a negative number. If x is -1, the base number ½ becomes 2. If x is -2, ½ becomes 4 (because 2² = 4). If x is -3, ½ becomes 8 (because 2³ = 8).

There's no shortcut. You have to evaluate each number and then add them. For example, there's no quick way to add 3^4 + 3^5. You have to evaluate each term and then add them.

1.10^-0.5 = 1 / (1.10^0.5) = 1.10^½ = √1.10 = 1.0488.

No, it doesn't work that way. First evaluate the factors of 3 and the factors of 4 separately, and then combine them by multiplication: (3²)(4^6) = (9)(4,096) = 36,864.

Here's a simple example: (2²)³ = (4)³ = 64.

First multiply a by b. That product becomes the exponent to be applied to 6.

Actually, x^(5/3) means the cube root of x^5. Alternatively, you can think of it as the 5th power of the cube root of x or (∛x)^5, i.e. x^(1/3) multiplied by itself 5 times = x^(1/3)×x^(1/3)×x^(1/3)×x^(1/3)×x^(1/3) = (x^(1/3))^5 = (∛x)^5.

Raise the first power to the second power. Then apply the new exponent to the base. For example, 3^(2²) = 3^4 = 81.

The easiest way to do it is first to find the fourth root of 81 and then find the cube of that number. It's not as hard as it sounds. The fourth root of 81 is 3. 3³ = 27. (Finding the fourth root means finding the square root of the square root. √81 = 9. √9 = 3.)