Section 6.1: Laws of Exponents
The laws of exponents describe how to handle expressions with the same base raised to powers.
Example 1
Simplify: \( x^3 \cdot x^5 \)
Using the product of powers rule: \( x^a \cdot x^b = x^{a+b} \)
\( x^3 \cdot x^5 = x^{3+5} = x^8 \)
Example 2
Simplify: \( \frac{y^7}{y^3} \)
Using the quotient of powers rule: \( \frac{x^a}{x^b} = x^{a-b} \)
\( \frac{y^7}{y^3} = y^{7-3} = y^4 \)
Example 3
Simplify: \( (z^2)^5 \)
Using the power of a power rule: \( (x^a)^b = x^{a \cdot b} \)
\( (z^2)^5 = z^{2\cdot5} = z^{10} \)
Practice Problems
- Simplify: \( a^4 \cdot a^6 \)
- Simplify: \( \frac{b^9}{b^4} \)
- Simplify: \( (c^3)^4 \)
- Simplify: \( x^5 \cdot x^0 \)
- Simplify: \( \frac{y^0}{y^3} \)