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}

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25.
Exponents
25.1
Product rule of exponents
25.2
Quotient rule of exponents
25.3
Power of a product rule
25.4
Power of a quotient rule
25.5
Power of a power rule
25.6
Negative exponent rule
25.7
Combining the exponent rules
25.8
Scientific notation
25.9
Convert between radicals and rational exponents
25.10
Solving for exponents
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