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12/3 - 2/15 का मान ज्ञात कीजिये।

Mathematics

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Answer

31316\dfrac{3^{13}}{16}

Step-by-step solution

5 steps

  1. Rewrite the denominator using the negative exponent rule 1a−n=an\frac{1}{a^{-n}} = a^{n}.

    12−23−15=12−2×315\frac{12^{-2}}{3^{-15}} = 12^{-2} \times 3^{15}

  2. Express 12 as a product of primes

    12=22×312 = 2^{2} \times 3.

    12−2=(22×3)−2=2−4×3−212^{-2} = (2^{2} \times 3)^{-2} = 2^{-4} \times 3^{-2}

  3. Substitute back into the expression.

    2−4×3−2×3152^{-4} \times 3^{-2} \times 3^{15}

  4. Combine the exponents for base 3.

    2−4×3−2+15=2−4×3132^{-4} \times 3^{-2 + 15} = 2^{-4} \times 3^{13}

  5. Rewrite using positive exponents in the denominator.

    2−4×313=31324=313162^{-4} \times 3^{13} = \frac{3^{13}}{2^{4}} = \frac{3^{13}}{16}

    Final answer: 31316\dfrac{3^{13}}{16}

    31316\boxed{\dfrac{3^{13}}{16}}
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