Question

Choose the equivalent expression with only positive exponents:

A) 10⁻² × 2⁻⁸²
B) 1/(10² × 2⁸)
C) 100/2⁻¹⁰⁴
D) 10²/2⁸

Answer 1

To choose the equivalent expression with only positive exponents, we need to simplify each expression and rewrite them with positive exponents. The equivalent expression with only positive exponents is Option B) 1/(10² × 2⁸).

Step-by-step explanation:

To choose the equivalent expression with only positive exponents, we need to simplify each expression and rewrite them with positive exponents.

Option B) 1/(10² × 2⁸) can be simplified as 1/((10²) × (2⁸)) = 1/(100 × 256) = 1/25600.

Option C) 100/2⁻¹⁰⁴ can be simplified as 100/1/(2¹⁰⁴) = 100 × (2¹⁰⁴) = 100 × 2(104) = 100 × (10²)⁴ = 100 × 10000 = 1000000.

Option D) 10²/2⁸ can be simplified as (10²)/(2⁸) = (100)/(256) = 0.39063.

Hence, the equivalent expression with only positive exponents is Option B) 1/(10² × 2⁸).