3 - 2/15 का मान ज्ञात कीजिये।

March 19, 2026Mathematics

ScanSolve AI Answer

March 19, 2026

Answer

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

Step 1: Rewrite the denominator using the negative exponent rule $\frac{1}{a^{-n}} = a^{n}$ .

\frac{12^{-2}}{3^{-15}} = 12^{-2} \times 3^{15}

Step 2: Express $12$ as a product of primes: $12 = 2^{2} \times 3$ .

12^{-2} = (2^{2} \times 3)^{-2} = 2^{-4} \times 3^{-2}

Step 3: Substitute back into the expression.

2^{-4} \times 3^{-2} \times 3^{15}

Step 4: Combine the exponents for base $3$ .

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

Step 5: Rewrite using positive exponents in the denominator.

2^{-4} \times 3^{13} = \frac{3^{13}}{2^{4}} = \frac{3^{13}}{16}

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

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

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Quick Answer

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.

Asked on March 19, 2026Mathematics

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 AnswerAnswered on March 19, 2026

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