Exponents Negative Exponents, Zero Exponents, Product of Powers, Quotient of Powers , Power to Power
Exponents are a way of representing repeated multiplication or division of a number or variable. They can be positive, negative, or zero.
Negative Exponents:
A negative exponent indicates the reciprocal of the number or variable raised to that power. For example, x^-3 is equal to 1/x^3. Negative exponents can also be written as fractions, such as 1/x^3.
Zero Exponents:
A zero exponent indicates that the number or variable is equal to 1. For example, x^0 = 1 for any value of x, as any number or variable raised to the power of 0 is always 1.
Product of Powers:
When multiplying two numbers or variables with the same base, you can add their exponents to simplify the expression. For example, x^3 * x^4 = x^(3+4) = x^7. This rule holds true for any number of factors being multiplied together.
Quotient of Powers:
When dividing two numbers or variables with the same base, you can subtract the exponent of the divisor from the exponent of the dividend to simplify the expression. For example, x^6 / x^3 = x^(6-3) = x^3. This rule holds true for any number of terms being divided.
Power to Power:
When raising a number or variable that is already raised to an exponent to another exponent, you can multiply the exponents together. For example, (x^3)^2 = x^(3*2) = x^6. This rule applies to both positive and negative exponents.
These rules of exponents can be used to simplify and solve equations involving exponential expressions.