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# Exponents
\\( x^n = x_1 \times x_2 \times\ \cdot\cdot\cdot\ \times x_n \\)
## Examples
* \\(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32 \\)
* \\(5^7 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 78125 \\)
# Exponent Operations
## Multiplication
If an exponented number is multiplied by another exponented number, the exponents would be summed together (instead of being multiplied)
\\( a^x \times b^y = (a \times b)^{x + y} \\)
* \\( 10^4 \times 2^2 = (10 \times 2)^{4 + 2} = 20^6 \\)
## Division
If an exponented number is multiplied by another exponented number, the exponents would be subtracted together (instead of being divided)
\\( a^x \div b^y = (a \div b)^{x - y} \\)
* \\( 10^3 \div 2^4 = (10 \div 2)^{(4 - 2)} = 5^2 = 25 \\)
## Exponent
If an exponented number is exponented, multiply the exponents together.
\\( (a^x)^y = a^{x \times y} \\)
* \\( (2^2)^3 = 2^{2 \times 3} = 2^6 = 64 \\)
# Special Exponents
Some exponents feel better than the other, and Mathemathics agrees with them.
## Zero Exponent
If a number is raised to the power of **zero**, the result is **one**.
\\( a^0 = 1 \\)
* \\( 5^0 = 1 \\)
* \\( 69.420^0 = 1 \\)
## Negative Exponent
If a number is raised to a negative power, also called as an inverse, it would be equal to...
\\( a^{-b} = \dfrac{1}{a^b} \\)
## Fractional Exponent
# Examples
## Exponential Equation
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