Exponent rules are mathematical rules that help us simplify and manipulate expressions with exponents. These rules make it easier to perform calculations involving powers.
1. Product Rule:
When multiplying two numbers with the same base, you add the exponents.
For example:
a^m * a^n = a^(m+n)
3^2 * 3^3 = 3^(2+3) = 3^5 = 243
2. Quotient Rule:
When dividing two numbers with the same base, you subtract the exponents.
For example:
a^m / a^n = a^(m-n)
10^4 / 10^2 = 10^(4-2) = 10^2 = 100
3. Power Rule:
When raising a power to another power, you multiply the exponents.
For example:
(a^m)^n = a^(m*n)
(2^3)^2 = 2^(3*2) = 2^6 = 64
4. Zero Exponent Rule:
Any number (except 0) raised to the power of 0 is always equal to 1.
For example:
a^0 = 1
5^0 = 1
5. Negative Exponent Rule:
A negative exponent indicates the reciprocal of the base raised to the positive exponent.
For example:
a^(-n) = 1 / a^n
2^(-2) = 1 / 2^2 = 1/4
6. Product of Powers Rule:
When multiplying powers with the same exponent, you multiply the bases.
For example:
(a * b)^n = a^n * b^n
(2 * 3)^4 = 2^4 * 3^4 = 16 * 81 = 1296
7. Quotient of Powers Rule:
When dividing powers with the same exponent, you divide the bases.
For example:
(a / b)^n = a^n / b^n
(10 / 5)^3 = 10^3 / 5^3 = 1000 / 125 = 8
These rules provide a systematic way to simplify expressions and perform calculations involving exponents. They are widely used in algebra and calculus to solve equations and manipulate mathematical expressions.
Explain the rules of exponents! You can make a chart, give examples, create a slideshow or a drawing or anything to show what you know about exponent rules!
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