Question

Evaluate the expression (4 × 10⁻⁴/² × 10²) using exponential rules and write the result in standard notation.

a) (2 × 10⁻⁶)
b) (2 × 10⁻²)
c) (8 × 10⁻⁶)
d) (8 × 10⁻²)

Answer 1

The expression (4 × 10⁻⁴) / (2 × 10²) evaluates to 2 × 10⁻⁶ in scientific notation and 0.000002 in standard notation by dividing the coefficients and subtracting the exponents of the powers of 10.

Step-by-step explanation:

To evaluate the expression (4 × 10⁻⁴) / (2 × 10²) using exponential rules, we start by dividing the coefficients and subtracting the exponents of the powers of 10:

• Divide the coefficients: 4 / 2 = 2.
• Subtract the exponents: (-4) - (2) = -6.

Combining these results, we get the expression in scientific notation: 2 × 10⁻⁶. This is the answer in scientific notation, but to express it in standard notation, we must move the decimal point 6 places to the left (because the exponent is negative), which gives us 0.000002.