Question

Click on all the expressions equivalent to 200×10³

a) 2×10⁵
b) 20×10⁴
c) 2000×10²
d) 200×1000

Answer 1

All the given options, 2×10µ (a), 20×10´ (b), 2000×10² (c), and 200×1000 (d) are equivalent to 200×10³. This is because in each case, you can manipulate the expressions using the rules of exponents to show they are the same as the original expression.

Step-by-step explanation:

The question requires us to identify the expressions equivalent to 200×10³. To do this, we can use the properties of exponents. Remember, when multiplying powers of 10, we add the exponents.

• 2×10µ: This is equivalent to 200×10³ because 2×10µ = 2×10²×10³ = 200×10³.
• 20×10´: This expression is equivalent to 200×10³ because 20×10´ = 2×10×10´ = 2×10µ, which we showed above is the same as 200×10³.
• 2000×10²: This also simplifies to 200×10³ as 2000×10² = 2×10×10³ = 200×10³.
• 200×1000: Here 10³ is expressed as 1000, so this is clearly the same as 200×10³.

Based on these calculations, all options a) 2×10µ b) 20×10´ c) 2000×10² d) 200×1000 are equivalent to 200×10³.