3 - 2/15 का मान ज्ञात कीजिये।

Mathematics
3 - 2/15 का मान ज्ञात कीजिये।

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Answer

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

Step 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}

Step 2: Express 1212 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}

Step 3: Substitute back into the expression.

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

Step 4: Combine the exponents for base 33.

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

Step 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}

\dfrac{3^{13}{16}}
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Rewrite the denominator using the negative exponent rule (1)/(a^-n) = a^n. 12^-23^-15 = 12^-2 × 3^15 Step 2: Express 12 as a product of primes: 12 = 2^2 × 3.

3 - 2/15 का मान ज्ञात कीजिये।
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Rewrite the denominator using the negative exponent rule (1)/(a^-n) = a^n. 12^-23^-15 = 12^-2 × 3^15 Step 2: Express 12 as a product of primes: 12 = 2^2 × 3. 12^-2 = (2^2 × 3)^-2 = 2^-4 × 3^-2 Step 3: Substitute back into the expression. 2^-4 × 3^-2 × 3^15 Step 4: Combine the exponents for base 3. 2^-4 × 3^-2 + 15 = 2^-4 × 3^13 Step 5: Rewrite using positive exponents in the denominator. 2^-4 × 3^13 = 3^132^4 = 3^1316 Final answer: 3^1316 3^1316