Question

Eight expressions are given below. Determine whether each expression is equivalent to 5^10 or not equivalent to 5^10.

Answer 1

See Explanation

Explanation:

The question is incomplete, as the 8 expressions are not given.

The general explanation is as follows

As complex as an expression may seem, you have to simplify each expression until it cannot be further simplified.

Then you categorize each result, depending on if it equals
`5^(10)` or not

Take for instance:

`5^5 * 5^5`

Using law of indices:

`5^5 * 5^5 = 5^{5+5`

`5^5 * 5^5 = 5^{10` ---- equivalent

`(5^5 + 5^5)/(2 * 5^(-5))`

Factorize the numerator

`(5^5 + 5^5)/(2 * 5^(-5)) = (5^5(1 + 1))/(2 * 5^(-5))`

`(5^5 + 5^5)/(2 * 5^(-5)) = (5^5 * 2)/(2 * 5^(-5))`

Cancel out 2

`(5^5 + 5^5)/(2 * 5^(-5)) = (5^5)/(5^(-5))`

Apply law of indices

`(5^5 + 5^5)/(2 * 5^(-5)) = 5^(5--5)`

`(5^5 + 5^5)/(2 * 5^(-5)) = 5^(5+5)`

`(5^5 + 5^5)/(2 * 5^(-5)) = 5^{10` ---equivalent

`125 * 78125`

Express as exponent

`125 * 78125 = 5^3 * 5^7`

Apply law of indices

`125 * 78125 = 5^{3+7`

`125 * 78125 = 5^{10` ---- equivalent

`5^3 + 5^7`

Solve exponents

`5^3 + 5^7 = 125 + 78125`

`5^3 + 5^7 = 78250` ---- not equivalent