1.2 Exponents and Radicals
Ideas in this lesson
- Laws of exponents
- Zero and negative exponents
- Radicals: evaluate and simplify
- Rational exponents
- Rationalizing the denominator
- Scientific notation
- Scientific measurements, units and scale
- Use and interpret radical and power models
- Justify exponent laws and test false rules
- Compare roots and investigate power patterns
Laws of exponents · Worked example
For \(x\ne0,\ y\ne0\), simplify \(\dfrac{6x^{9}y^{5}}{18x^{3}y^{3}}\).
Answer: \(\dfrac{x^{6} y^{2}}{3}\)
Reduce the coefficients: \(\dfrac{6}{18}=\dfrac{1}{3}\).
Subtract exponents only for equal bases: \(x^{9-3}=x^{6}\) and \(y^{5-3}=y^{2}\).
Combine these factors to obtain \(\dfrac{x^{6} y^{2}}{3}\); the stated restrictions still apply.
Subtract exponents only for equal bases: \(x^{9-3}=x^{6}\) and \(y^{5-3}=y^{2}\).
Combine these factors to obtain \(\dfrac{x^{6} y^{2}}{3}\); the stated restrictions still apply.