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2GM²/r² × m/r² ÷ 6m²/8r⁴

Physics

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Answer

12mnr4\frac{12mn}{r^4}

Step-by-step solution

5 steps

  1. Rewrite the division as multiplication by the reciprocal of the third fraction.

    9m2rr3×mr2÷6m2r48nr4=9m2rr3×mr2×8nr46m2r4\frac{9m^2r}{r^3} \times \frac{m}{r^2} \div \frac{6m^2r^4}{8nr^4} = \frac{9m^2r}{r^3} \times \frac{m}{r^2} \times \frac{8nr^4}{6m^2r^4}

  2. Multiply the numerators and the denominators.

    9m2r⋅m⋅8nr4r3⋅r2⋅6m2r4\frac{9m^2r \cdot m \cdot 8nr^4}{r^3 \cdot r^2 \cdot 6m^2r^4}

  3. Combine like terms in the numerator and denominator using exponent rules (ax⋅ay=ax+ya^x \cdot a^y = a^{x+y}).

    (9⋅8)⋅(m2⋅m)⋅(r⋅n⋅r4)(6)⋅(r3⋅r2⋅r4)⋅(m2)\frac{(9 \cdot 8) \cdot (m^2 \cdot m) \cdot (r \cdot n \cdot r^4)}{(6) \cdot (r^3 \cdot r^2 \cdot r^4) \cdot (m^2)} 72m2+1nr1+46m2r3+2+4\frac{72 m^{2+1} n r^{1+4}}{6 m^2 r^{3+2+4}} 72m3nr56m2r9\frac{72 m^3 n r^5}{6 m^2 r^9}

  4. Simplify the numerical coefficients and variables using exponent rules (axay=ax−y\frac{a^x}{a^y} = a^{x-y}).

    726⋅m3m2⋅n⋅r5r9\frac{72}{6} \cdot \frac{m^3}{m^2} \cdot n \cdot \frac{r^5}{r^9} 12⋅m3−2⋅n⋅r5−912 \cdot m^{3-2} \cdot n \cdot r^{5-9} 12⋅m1⋅n⋅r−412 \cdot m^1 \cdot n \cdot r^{-4}

  5. Express the term with a negative exponent as a reciprocal.

    12mn⋅1r412mn \cdot \frac{1}{r^4} 12mnr4\frac{12mn}{r^4}
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