Question

Is the equation 3−5⋅(81√4)33−4=3−6
true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

False. The numerator simplifies to 3−2
and 3−23−4≠3−6
.
False. The numerator simplifies to 3 to the negative 2 power and the fraction with numerator 3 to the negative 2 power and denominator 3 to the negative 4 power is not equal to 3 to the negative 6 power.

False. (81−−√4)3
cannot be determined.
False. open paren 4th root of 81 close paren cubedcannot be determined.

True. (81−−√4)3=32
and 3−103−4=3−6

True. open paren 4th root of 81 close paren cubed is equal to 3 squared and the fraction with numerator 3 to the negative 10 power and denominator 3 to the negative 4 power is equal to 3 to the negative 6 power

True. The numerator simplifies to 3−2
and 3−23−4≠3−6
.

Answer 1

False.

Compute (81^(1/4))^3: 81 = 3^4 so 4th root of 81 is 3, and (3)^3 = 3^3. Then
3^(−5)·(81^(1/4))^3 = 3^(−5)·3^3 = 3^(−2).
Dividing by 3^(−4) gives 3^(−2−(−4)) = 3^2 = 9, which is not 3^(−6). Hence the equation is false.