16⁻² × 5² × 3⁻⁴ / (25² × 2⁴ × 27⁻²)

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Apply the power rule (a^m)ⁿ = a^(mn) to simplify the terms in the numerator and denominator. ((2⁴)⁻² × 5² × 3⁻⁴)/((5²)² × 2⁴ × (3³)⁻²) = (2^(4 × (−2)) × 5² × 3⁻⁴)/(5^(2 × 2) × 2⁴ × 3^(3 × (−2))); = (2⁻⁸ × 5² × 3⁻⁴)/(5⁴ × 2⁴ × 3⁻⁶); Step 2: Group terms with the same base and apply the division rule for exponents, (a^m)/(aⁿ) = a^(m−n). 2⁻⁸⁻⁴ × 5²⁻⁴ × 3⁻⁴⁻⁽⁻⁶⁾ Step 3: Simplify the exponents. 2⁻¹² × 5⁻² × 3⁻⁴⁺⁶ 2⁻¹² × 5⁻² × 3² The simplified expression is: 2⁻¹² × 5⁻² × 3²

16⁻² * 5² * 3⁻⁴ / (25² * 2⁴ * 27⁻²)

Answer

Step-by-step solution

Apply the power rule $(a^m)^n = a^{mn}$ to simplify the terms in the numerator and denominator.

Group terms with the same base and apply the division rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$ .

Simplify the exponents.

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