Question

Andre and Elena knew that after 28 days they would have 2²⁸ coins, but they wanted to find out how many coins that actually is. Andre wrote: 2 28 = 56. Elena said, "No, exponents mean repeated multiplication. It should be 28 28, which works out to be 784." Do you agree with either of them? Explain your reasoning.

Answer 1

I agree with none of them

Explanation:

Given

`Expression= 2^(28)`

`Andre: 2 * 28 = 56`

`Elena: 28 * 28 = 756`

Required

Who is correct?

`Expression= 2^(28)`

When we apply law of indices to the above, it gives 2 multiplies by itself in 28 places

i.e.

`Expression= 2^(28)`

`Expression= 2*2*2*..........*2` ---- in 28 places

Andre's interpretation of the expression is incorrect as:

`2^(28) \\eq 56`

Also, Elena's expression is incorrect.

This is so, because

`2^28 \\eq 28*28`

Hence, both of them are incorrect and I agree with none of them