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bruin61579
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Tue Mar 29, 2011 1:39 pm
Hi,
I just took a Knewton practice test, and this was a PS question. I'm putting <> around the exponent, since the formatting didn't translate when I pasted:
3 + 3 + 3 + 2 × 3<2> + 2 × 3<3> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7> =
The explanation Knewton posts is as follows:
The key to this problem is realizing that 3 + 3 + 3 = 9 = 3<2>. Let us rewrite the prompt accordingly: 3<2> + 2 × 3<2> + 2 × 3<3> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7> =
Now, since this equation contains exponents, we should try to manipulate the terms so that we can use the exponent rules we know. We can rewrite the first three terms as 3<2> + 3<2 >+ 3<2.> This is equivalent to 3(3<2>) = 3<1>(3<2>) = 3<3>.
The equation can thus be simplified: 3<3> + 2 × 3<3> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7>.
Since 3 × 3<3> = 3<4>, we can simplify further: 3<4> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7>.
We repeat this procedure until we get: 3 × 3<7> = 3<8>.
The explanation overall is confusing for some reason, specifically I don't understand what happens to the 2s in the equation - they seem to just drop off.
Thanks,
David
I just took a Knewton practice test, and this was a PS question. I'm putting <> around the exponent, since the formatting didn't translate when I pasted:
3 + 3 + 3 + 2 × 3<2> + 2 × 3<3> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7> =
The explanation Knewton posts is as follows:
The key to this problem is realizing that 3 + 3 + 3 = 9 = 3<2>. Let us rewrite the prompt accordingly: 3<2> + 2 × 3<2> + 2 × 3<3> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7> =
Now, since this equation contains exponents, we should try to manipulate the terms so that we can use the exponent rules we know. We can rewrite the first three terms as 3<2> + 3<2 >+ 3<2.> This is equivalent to 3(3<2>) = 3<1>(3<2>) = 3<3>.
The equation can thus be simplified: 3<3> + 2 × 3<3> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7>.
Since 3 × 3<3> = 3<4>, we can simplify further: 3<4> + 2 × 3<4> + 2 × 3<5> + 2 × 3<6> + 2 × 3<7>.
We repeat this procedure until we get: 3 × 3<7> = 3<8>.
The explanation overall is confusing for some reason, specifically I don't understand what happens to the 2s in the equation - they seem to just drop off.
Thanks,
David
