Final answer:
To simplify 3⁵ × 3² / 3⁻⁶, add the exponents of the numerator and then subtract the exponent of the denominator resulting in a single power of 3¹³.
Step-by-step explanation:
The question involves the manipulation of exponents, specifically using the laws of exponents to combine powers of the same base. Remember that when you multiply powers with the same base, you add the exponents, and when you divide them, you subtract the exponents. To solve the given expression 3⁵ × 3² / 3⁻⁶, we use these rules:
- First, add the exponents of the terms that are being multiplied: 5 (from 3⁵) + 2 (from 3²) = 7.
- Next, subtract the exponent of the denominator (since it is division) which is -6 (from 3⁻⁶): 7 - (-6) = 7 + 6 = 13.
- The combined expression can thus be written as a single power: 3¹³.
The laws of exponents make it much simpler to handle large exponential expressions without needing to write out all the individual multiplications. Calculators easily compute such exponentials, but understanding the process is crucial to ensure you can solve them without technological aid.