Exponential Terms and Exponents Quiz

Exponent rules are mathematical rules that govern the manipulation of expressions with exponents. They can be used to simplify equations by applying properties such as the product rule, quotient rule, power rule, and zero rule.

In an exponential expression, the base is the number being multiplied repeatedly, while the exponent is the number that indicates how many times the base should be multiplied by itself.

Writing equations in exponential form helps to simplify the equations and make them easier to read and understand. It also allows for the application of exponent rules to manipulate the equations more efficiently.

When multiplying exponentials with the same base, you add their exponents. For example, $(x^2)(x^3) = x^5$.

When you have a power to a power, you multiply the exponents. For example, $(x^2)^4 = x^8$.

When dividing exponentials with the same base, you subtract the exponents. For example, $(x^4)/(x^3) = x^1$.

When you have a product of a power, you give each base its own exponent. For example, $(xy)^2 = x^2y^2$.

When you have a quotient to a power, each base in the quotient gets raised to that power.

The result of distributing the exponent to each part of the fraction is (x^3) / (y^3).

The five properties of exponents are: product of powers, power of a product, quotient of powers, power of a quotient, and negative exponent.

The seven exponent rules, or laws of exponents, that students need to learn are: 1. Product Rule 2. Quotient Rule 3. Power Rule 4. Zero Rule 5. Negative Exponent Rule 6. Distributive Rule 7. Simplifying Rule.

To solve an equation where two bases of the same value are being multiplied, keep the bases the same and add the exponents together.

To divide two bases of the same value in an equation, keep the base the same and subtract the exponent values.

When a power is being raised by another power, the exponents are multiplied together and the base remains the same.

The seven basic rules that explain how to solve most math equations that involve exponents are: 1) Product of Powers Property, 2) Power of a Power Property, 3) Quotient of Powers Property, 4) Power of a Product Property, 5) Power of a Quotient Property, 6) Zero Exponent Property, and 7) Negative Exponent Property.

The product of powers property states that when two power expressions of the same base are multiplied, the result is given by repeating the base and raising it to the sum of the exponents.

The power of a power property states that when a power expression is raised by another power, the two exponents involved must be multiplied and that power is applied to the original base.

The quotient of powers property states that in division between two power expressions of the same base, the result is given by repeating the base raised to the subtraction of the exponents.

The power of a product property states that when multiplying two values raised by a power, the result can be found by multiplying the quantities, each raised by the same original power. For example: $(x*y)^n = x^n * y^n$.

The power of a quotient property states that when dividing two quantities raised by a power, the result can be found by dividing the numerator and denominator, both raised by the same original power. For example: $(\frac xy)^n = \frac {x^n},{y^n}$.

The power of a power property states that when a power expression is raised by another power, the two exponents involved must be multiplied and that power is applied to the original base. For example: $(x^n)^m = x^{n*m}$.

The quotient of powers property states that when dividing two power expressions of the same base, the result is given by repeating the base raised to the subtraction of the exponents. For example: $\frac {x^n},{x^m} = x^{n-m}$.