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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15.
Exponents
15.1
Product rule of exponents
15.2
Quotient rule of exponents
15.3
Power of a product rule
15.4
Power of a quotient rule
15.5
Power of a power rule
15.6
Negative exponent rule
15.7
Combining the exponent rules
15.8
Scientific notation
15.9
Convert between radicals and rational exponents
15.10
Solving for exponents
NZ Year 10 Maths
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