student writes down the following as part of her response:

[stepha1275]

student writes down the following as part of her response:

a ) 32 ´ 33 = 729. and

b) 3 -2 = -9.

Are her answers correct? If not, explain why you think her answers are incorrect. Include in your explanation what she did wrong, if any. What would you advise her to do instead?

 

[soroban]

Hello, stepha1275!

student writes down the following as part of her response:

a ) 32 ´ 33 = 729. and

b) 3 -2 = -9.

Are her answers correct? If not, explain why you think her answers are incorrect.
Include in your explanation what she did wrong, if any.
What would you advise her to do instead?

first, I'd advise her to learn to write math expressions clearly.

As they are written, the "equations" are obviously false.

. . \(\displaystyle 32 \times 33 \:=\:1056\text{ . . . and not 729}\)

. . \(\displaystyle 3 - 2 \:=\:1\text{ . . . and not -9}\)


I am guessing that exponents are intended . . .


The first one might be: .\(\displaystyle 3^2\cdot3^3\)

Then the answer is: .\(\displaystyle 3^2\cdot3^3 \;=\;3^{2+3} \;=\;3^5 \;=\;243\)

She probably multiplied the exponents:
. . \(\displaystyle 3^2\cdot3^3 \;=\;3^{2\cdot3} \;=\;3^6 \;=\;729\) . . . wrong!


The second could be: .\(\displaystyle 3^{-2}\)

Then the answer is: .\(\displaystyle 3^{-2} \;=\;\tfrac{1}{3^2} \;=\;\tfrac{1}{9}\)

She probably thought that a negative exponent makes the number negative.
. . Something like: .\(\displaystyle 3^{-2} \;=\;-(3^2) \;=\;-9\) . . . wrong!