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What is an Exponent?
Exponent is used in the exponentiation expression, which tells how many times a number (base) is multiplied by itself. Exponent is written at the upper right-hand corner of the base and mathematically represented as “an or bn”.
In this exponentiation expression “a & b” are known as the base and “n” is known as the exponent or power. This “n” power is positive or negative and works as a deciding factor to repeat the multiplication of the base for the respective exponent.
For example:
- If the exponent of 5 is 3 then 5³ = 5 × 5 × 5 = 125.
- “x²”means it multiplies two times such as: x × x and 4² = 4 × 4 = 16.
Laws of Exponents
Before the solution of any exponentiation expression you have to be familiar with basic exponent laws & rules:
- If the two numbers are multiplied together with the same base but different exponents then it is solved by adding the exponent such as: an × am= a(n+m).
- If the exponent is negative then it can removed by reciprocating the base and raising the exponent with a positive sign. i.e., a(-n)= 1/an.
- If exponents of any base are raised to another exponent, then exponents are multiplied together. i.e., (am)n= a(m × n).
- When two bases are raised by a single power then power is distributed on both bases such as: (a × b)n= an × bn & (a/b)n = an/bn.
- If the value of exponent is 1 then it returns the same base. i.e., a1= a.
- If the exponent of any base is “0” then its value is always “1” (i.e., a0= 1). Moreover, “00” is undefined, sometimes conventionally taken as 1.
How to Solve Exponents?
For quick solutions of exponentiation expression use the exponents calculator. However, if you want to solve it by hand then do so by the below steps:
- Note the base & exponent from the given expression.
- Now, write the base number of times as the exponent indicates with a multiplication sign. i.e., 35=3 × 3 × 3 × 3 × 3.
- If “n” is positive: an= a × a × ... × a (n times)
- If “n” is negative: a-n= (1/a)n = (1/a) × (1/a) × (1/a) ×… × (1/a) (n times)
- Finally, multiply all repeated bases and get the final exponent value. i.e., 3 × 3 × 3 × 3 × 3 = 243.
With these steps, calculating the exponent value for small numbers is easy. But it is quite difficult if the exponent & base is a large number, decimals, or negative. To remove this difficulty use our base calculator and get accurate results for any base or exponent.
Example:
Find a value of 2 to the power of 5.
The 2 raised to the power 5 is written as: 25 = 2 × 2 × 2 × 2 × 2 = 32.
What is 3 to the power of 2?
The “3 to the power of 2 is “9” and mathematically written as: 32 = 3 × 3 = 9.
Find the value of “-3 raised to the power of 3”.
It is written as: (-3)3 = -3 × -3 × -3 = -27.
Important Exponents Values
Here we provided some important results of exponentiation expressions for positive, negative, and decimal exponents by using the above exponential calculator.
| What is | Exponentiation Expression | Exponents Value |
|---|---|---|
| 2 to the power of 5 | 25 | 25 = 2×2×2×2×2 = 32 |
| 2 to the power of 6 | 26 | 26 = 2×2×2×2×2×2 = 64 |
| 3 to the power of 4 | 34 | 34= 3×3×3×3 = 81 |
| 3 to the power of 5 | 35 | 35 = 3×3×3×3×3 = 243 |
| 4 to the power of 2 | 42 | 4² = 4×4 = 16 |
| 7 to the power of 6 | 76 | 76=7×7×7×7×7×7= 117649 |
| 8 to the power of 5 | 85 | 85 = 8×8×8×8×8 = 32768 |
| 0.5 to the power of 2 | 0.52 | 0.52 = 0.5 × 0.5 = 0.25 |
| 1.5 to the power of 3 | 1.53 | 1.53= 1.5×1.5× 1.5 = 3.375 |
| -5 to the power of 4 | -54 | -54 = -5×-5×-5×-5= 625 |
| 5 to the power of -4 | 5⁻⁴ | 5⁻⁴= 1/5×1/5×1/5×1/5= 0.0016 |
| 10 to the power of 0 | 100 | 100 = 1 |
FAQ’s About Exponents
What is base and exponent?
In any exponential number or expression like an, a is known the base (number being multiplied), and “n” is called exponent or power (tells how many times the base is multiplied).
What is value of “6 with exponent of 4”?
The value of 6 with an exponent of 4 is 1296 and mathematically can be represented as: 64 = 6 × 6 × 6 × 6 = 1296. Also, use our above power calculator for quick calculation or verification of exponent results for any base & power.
How to multiply & divide exponents?
For multiplication of the same bases, add the powers of the given expression. i.e., multiply 23 by 22 is 23+2= 25= 2 × 2 × 2 × 2 × 2 = 32. But, for the division of exponents with the same bases, you have to subtract the exponent of a given number. i.e., Divide 37 by 34, we get: 37-4 = 33 = 3 × 3 × 3 = 27.
Can this exponential calculator solve negative, decimal, or fractional exponents?
Yes, our exponent calculator is an advanced tool that finds the value of any expression, whether an exponential expression having a small, large, negative, decimal, or fractional exponent & base. i.e., 2⁻³ = 0.125 & 91/2= 3.
How to solve negative exponent?
For a quick solution, you can use our negative exponent calculator. But for a manual solution, note the base & exponent and take the reciprocal of the base to convert negative sign into positive. Then multiply by repeating the number according to power.
How to find value of fractional exponents?
In fractional exponent, the power of a number in fraction form is like 1/n. It is solved by taking the nth-root of a number. i.e., 21/2 = √2, 21/3 = ³√2, and so on. Also, use the fraction exponent calculator by writing the base & power separately.
