Which could have been the original exponential form of the expression Dawn simplified? Check all that apply.

$(-4)^3$
$2^6$
$3^4$
$(-8)^2$
$(-2)^6$

Evaluate each exponential expression.
Compare the values of the expressions.
Identify the expressions with the same value.
The expressions 2 6 , ( − 8 ) 2 , and ( − 2 ) 6 all equal 64, so the answer is 2 6 , ( − 8 ) 2 , ( − 2 ) 6 ​ .

Explanation

Evaluate the expressions We need to evaluate each of the given exponential expressions and identify which ones have the same value.

Calculating the values Let's evaluate each expression:


( − 4 ) 3 = − 4 × − 4 × − 4 = − 64
2 6 = 2 × 2 × 2 × 2 × 2 × 2 = 64
3 4 = 3 × 3 × 3 × 3 = 81
( − 8 ) 2 = − 8 × − 8 = 64
( − 2 ) 6 = − 2 × − 2 × − 2 × − 2 × − 2 × − 2 = 64

Comparing the results Comparing the values, we see that 2 6 , ( − 8 ) 2 , and ( − 2 ) 6 all equal 64. The expression ( − 4 ) 3 equals -64, and 3 4 equals 81.

Final Answer Therefore, the original exponential form of the expression Dawn simplified could have been 2 6 , ( − 8 ) 2 , or ( − 2 ) 6 .


Examples
Exponential forms are used in various fields, such as calculating compound interest, population growth, and radioactive decay. For instance, if a population doubles every year, the population after n years can be represented as P = P 0 ​ × 2 n , where P 0 ​ is the initial population. Understanding exponential forms helps in predicting future values in such scenarios.

Answered by GinnyAnswer | 2025-07-08