Question

Drawing Conclusions

Consider the expression.

6•6^0•6^-3

Which statements are true about the expression? Check all that apply.

The 6 without an exponent is equivalent to the 6 having a 0 exponent.

The sum of the exponents is 2.

Multiply the exponents to simplify the expression.

The expression has a value of -

An equivalent expression is 65.6-7

Answer 1

The last two or d and e

Answer 2

Some of the Exponents = -2 that is true, not 2.

Explanation:

Let's check one at a time.

(a)The 6 without an exponent is equivalent to the 6 having a 0 exponent.

`6^(0) =1` and
`6^(1)` = 6 (no exponent. 6
`\\eq` 1 therefore this statement is False.

(b)The sum of the exponents is -2.

let's check , if the base is same we can add the exponents that is the exponent rule.(well established).

if we add exponents in the given expression we get.

`6^(1) 6^(0) 6^(3) =6^(1+0+(-3)) =6^(-2)`, therefore we can see that the sum of the exponents = -2 this is true.

(c) An equivalent expression is 65.6-7, lets evaluate our above expression, it is equal to
`(1)/(36)` which we can see that
`(1)/(36) \\eq 65.6-7` ,therefore this statement is false as well.