Final answer:
One eighth of 1,000 is 125, and when multiplying exponents like 3².35, we add the exponents to get 37. For division involving powers of ten, subtract the exponents as in the case of (8.552 × 10⁶) ÷ (3.129 × 10³) equalling 10².
Step-by-step explanation:
Understanding Division and Exponents
When calculating one eighth of 1,000, we can use the reciprocal method, which gives us 125. In the case of 3².35, we use the rule xⁿ×x⁹ = x(p+q), which results in 37. While handling calculations like 8.552 × 10⁶ divided by 3.129 × 10³, we subtract the exponents, resulting in 10². Division also applies to negative exponents and can be simplified using standard rules.
For instance, when dividing 2.4 × 10¹³ by 8 × 10⁷, we first subtract the exponents and then adjust the prefactor to comply with the proper decimal form, which in this case would give us 24 × 10⁶.To divide the expression (125 - 8x³) by (25 + 10x + 4x²), we can use long division. Here are the steps:
Start by dividing the highest degree terms. Divide 125 by 25, which gives us 5.
Multiply 5 by (25 + 10x + 4x²), which gives us 125 + 50x + 20x².
Subtract (125 + 50x + 20x²) from (125 - 8x³). This gives us -8x³ - 50x - 20x².
Bring down the next term, which is -8x³.
Divide -8x³ by 25, which gives us -0.32x³.
Multiply -0.32x³ by (25 + 10x + 4x²), which gives us -8x³ - 3.2x⁴ - 1.28x⁵.
Subtract (-8x³ - 3.2x⁴ - 1.28x⁵) from (-8x³ - 50x - 20x²). This gives us 3.2x⁴ + 50x + 20x².
So, the quotient of (125 - 8x³) divided by (25 + 10x + 4x²) is 5 - 0.32x³ + 3.2x⁴ + 50x + 20x².