Laws of Exponents
Grade 8 math lesson on the laws of exponents including product rule, quotient rule, and power rule. Students learn to simplify expressions with exponents by applying the multiplication, division, and power rules for working with bases raised to integer powers.
Key Concepts
New Concept The Laws of Exponents are rules that simplify expressions involving powers with the same base. Here are the three fundamental laws:.
$x^a \cdot x^b = x^{a+b}$ $\frac{x^a}{x^b} = x^{a b} \quad \text{for} x≠0 $ $(x^a)^b = x^{ab}$ What’s next Next, we'll break down these laws with worked examples for multiplication, division, and raising a power to a power, building your problem solving speed.
Common Questions
What are the laws of exponents?
The main laws of exponents are: product rule (x^a times x^b = x^(a+b)), quotient rule (x^a divided by x^b = x^(a-b)), power rule ((x^a)^b = x^(ab)), zero exponent rule (x^0 = 1), and negative exponent rule (x^(-a) = 1/x^a).
How do you multiply numbers with the same base?
When multiplying numbers with the same base, keep the base and add the exponents. For example, x^3 times x^4 = x^7 because 3 + 4 = 7.
How do you divide numbers with exponents?
When dividing numbers with the same base, keep the base and subtract the exponents. For example, x^7 divided by x^3 = x^4 because 7 - 3 = 4.
What does x^0 equal and why?
Any number raised to the zero power equals 1 (except 0^0 which is undefined). This follows from the quotient rule: x^n divided by x^n = x^(n-n) = x^0 = 1, since any number divided by itself is 1.