Question

Which expressions are equivalent to 2^5•2^4? Check all that apply.

Answer 1

AEF

Explanation:

Answer 2

Option A:
`2^9`

Option E:
`2^(-2).2^(11)`

Option F:
`(2.2.2.2.2)(2.2.2.2)`

Solution:

Given expression is
`2^5.2^4`.

To find which expression is equivalent to the given expression.

Option A:
`2^9`

Using exponent rule:
`a^b.a^c=a^((b+c))`

`2^5.2^4=2^((5+4))=2^9`

Therefore
`2^9` is equivalent to the given expression.

Option B:
`2^(20)`

It is not equivalent to the given expression.

Option C:
`2.2^9`

`2.2^9=2^((1+9))=2^(10)`

Therefore, It is not equivalent to the given expression.

Option D:
`2^(10).2^2`

`2^(10).2^2=2^((10+2))=2^(12)`

Therefore, It is not equivalent to the given expression.

Option E:
`2^(-2).2^(11)`

`2^(-2).2^(11)=2^((2-11))=2^9`

Therefore, It is equivalent to the given expression.

Option F:
`(2.2.2.2.2)(2.2.2.2)`

`(2.2.2.2.2)(2.2.2.2)=2^5.2^4`

Therefore, It is equivalent to the given expression.

Hence option A, Option E and Option E are equivalent to the given expression.