Given: A = (0.08x10⁻³ x (102)3) / (0.2x0.1x103) ; B = 0.0025 × 10⁻⁸ and C = −32 + 4 × 5 + (22-3)25 - 1. 1)…

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Given: A = (0.08x10⁻³ x (102)3) / (0.2x0.1x103) ; B = 0.0025 × 10⁻⁸ and C = −32 + 4 × 5 + (22-3)25 - 1. 1) Write A in the form a x 10ⁿ, where a and n are integers. 2) Write B in scientific notations. 3) Show that C is a prime number.

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V. 1) To write A in the form a × 10ⁿ: Step 1: Simplify the numerator and denominator separately. A = (0.08 × 10⁻³ × (10²)³)/(0.2 × 0.1 × 10³); Numerator: 0.08 × 10⁻³ × 10^(2 × 3) = 0.08 × 10⁻³ × 10⁶ = 0.08 × 10⁽⁻³⁺⁶⁾ = 0.08 × 10³; Denominator: 0.2 × 0.1 × 10³ = 0.02 × 10³ Step 2: Divide the simplified numerator by the simplified denominator. A = (0.08 × 10³)/(0.02 × 10³) = 0.08/0.02 × (10³)/(10³) = 4 × 1; A = 4 Step 3: Express A in the form a × 10ⁿ where a and n are integers. A = 4 × 10⁰ 2) To write B in scientific notation: Given B = 0.0025 × 10⁻⁸. Step 1: Convert 0.0025 into scientific notation. To move the decimal point 3 places to the right to get 2.5, we multiply by 10⁻³. 0.0025 = 2.5 × 10⁻³ Step 2: Substitute this back into the expression for B. B = (2.5 × 10⁻³) × 10⁻⁸; B = 2.5 × 10⁽⁻³⁻⁸⁾; B = 2.5 × 10⁻¹¹ 3) To show that C is a prime number: Given C = −3² + 4 × 5 + (2² − 3)²⁵ − 1. Step 1: Evaluate each term according to the order of operations. −3² = −(3 × 3) = −9; 4 × 5 = 20; (2² − 3)²⁵ = (4 − 3)²⁵ = (1)²⁵ = 1 Step 2: Substitute these values back into the expression for C. C = −9 + 20 + 1 − 1 Step 3: Calculate the value of C. C = 11 + 1 − 1; C = 12 − 1; C = 11; Step 4: Determine if C=11 is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 11 is greater than 1, and its only positive divisors are 1 and 11. Therefore, C=11 is a prime number.

Given: A = (0.08x10⁻³ x (102)3) / (0.2x0.1x103) ; B = 0.0025 x 10⁻⁸ and C = -32 + 4 x 5 + (22-3)25 - 1. 1) Write A in the form a x 10ⁿ, where a and n are integers. 2) Write B in scientific notations. 3) Show that C is a prime number.

Step-by-step solution

Simplify the numerator and denominator separately.

Divide the simplified numerator by the simplified denominator.

Express $A$ in the form $a \times 10^n$ where $a$ and $n$ are integers.

Convert 0.0025 into scientific notation.

Substitute this back into the expression for $B$ .

Evaluate each term according to the order of operations.

Substitute these values back into the expression for $C$ .

Calculate the value of $C$ .

Determine if $C=11$ is a prime number.

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