Final answer:
When dividing powers of the same base, subtract the exponents. For the expression 4^2 / 4^6 4^(-3) 4^3 4^(-4) 4^4, after subtracting exponents the result is 4^10. This is achieved using the law of exponent division.
Step-by-step explanation:
The question involves dividing powers of the same base, which in this case is the number 4. When you divide exponential terms with the same base, you can simplify the expression by subtracting the exponents. This is because of the law of exponents which states that am ÷ an = am-n. Using this rule, we can combine the expression 42 ÷ 46 4–3 43 4–4 44 into a single term with a power of 4.
To solve, you would follow this process:
- Combine all terms by subtracting the exponents of the terms in the denominator from the corresponding exponents in the numerator.
- This leads to: 42 × 4–6 × 43 × 4–3 × 4–4 × 44. The negative signs indicate division by those terms.
- Simplify the expression by adding and subtracting exponents: 4(2 - 6 + 3 - (-3) - (-4) + 4).
- Calculate the resulting exponent: 4(2 - 6 + 3 + 3 + 4 + 4) = 410.
Therefore, when dividing these exponential terms, the result is 410.