Question

Rewrite each side of the equation 2013 - 2 × 5² in a common base.

Options:
a) 2013 - 50
b) 2013 - 500
c) 1961
d) 1913

Answer 1

After calculating 5² as 25 and multiplying by 2 to get 50, we subtract 50 from 2013 to arrive at the simplified expression 2013 - 50, which equals 1963.

Step-by-step explanation:

I will rewrite each side of the equation 2013 - 2 × 5² in a common base. First, we need to calculate 5², which means 5 raised to the power of 2. Using our mathematical knowledge of squares and other powers, we know that:

5² = 5 × 5 = 25

Now, we proceed to compute 2 × 5²:

2 × 25 = 50

Hence, the equation 2013 - 2 × 5² can be rewritten as:

2013 - 50

When we subtract 50 from 2013, we get:

2013 - 50 = 1963

Therefore, the correct answer is option a) 2013 - 50, which simplifies down to 1963.