Combining the exponent rules

Combining the exponent rules

We have now learned all individual exponent rules in the previous sessions. In this session, we will try to use different exponent rules to solve problems.
Basic Concepts: Product rule of exponents, Quotient rule of exponents, Power of a product rule , Power of a quotient rule , Power of a power rule , Negative exponent rule
Related Concepts: Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}, Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}, Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}, Exponents: Negative exponents

Lessons

  • Introduction
    What are exponent rules?
  • 1.
    Simplify the following and write the answer with positive exponents
    a)
    ((−16a5b−3)(3a3b5)2a2b−2)3 (\frac{(-16a^5b^{-3}) (3a^3b^5)}{2a^2b^{-2}} {)^3}

    b)
    ((x3y+5)(x4y−2)xy+3)( \frac{(x^{3y+5}) (x^{4y-2})}{x^{y+3}} )

    c)
    (−3x5y4z9)−3(−5x4y−3z11)4(-3{x^5}{y^4}{z^9}{)^{-3}} (-5 {x^4}{y^{-3}}{z^{11}}{)^4}

Do better in math today
Get Started Now
26.
Exponents
26.1
Product rule of exponents
26.2
Quotient rule of exponents
26.3
Power of a product rule
26.4
Power of a quotient rule
26.5
Power of a power rule
26.6
Negative exponent rule
26.7
Combining the exponent rules
26.8
Scientific notation
26.9
Convert between radicals and rational exponents
26.10
Solving for exponents
ACCUPLACER Test Prep
Don't just watch, practice makes perfect