#Can someone explain, how they compared this please, thanks
raw lynx
final finchBOT
opal dagger
The same way the answer says.
16 = 2^4 (2 x 2 x 2 x 2 = 16)
8 = 2^3 (2 x 2 x 2 = 8)
4 = 2^2 (2 x 2 = 4)
This becomes:
(2^4)^2; 2^21; (2^3)^6; (2^2)^10,
then from the rule (a^n)^m = a^(nxm) it becomes
2^(4x2); 2^21; 2^(3x6); 2^(2x10)
which is
2^8; 2^21; 2^18; 2^20.
For powers of 2 (or any number greater than 1), the largest power is the biggest number. The largest power here is 21, so the answer is 2^21.
raw lynx
what part of it don't you understand
They are not telling me what they're doing, you may understand without but I don't
heady laurel
so yeah that's my question, what part of it don't you understand
it's fine that you don't understand it but where do I start explaining
raw lynx
What did they do, the opposite of the formula?
unborn schooner
They make all the number 2^X by using the yellow box. then they pick the highest X.
opal dagger
You just convert the bases (16, 2, 8 and 4) into the form of 2^n.
raw lynx
@heady laurel @unborn schooner @opal dagger Are you all able to synthesize a formula for me to use?
Because in the comparison questions I don't see (a^n)^m only a^n
keen valley
8 = 2^3
raw lynx
@unborn schooner @opal dagger @keen valley @heady laurel
Comparing Exponential Numbers
eg. 16², 2²¹, 8⁶, 4¹⁰
- Rewrite, 16^2 as a power of 2
- 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16
16 = 2⁴
- Replace 16² w/ 2⁴
- Add the power of the original
- ² = (2⁴)²
- Apply the rule
Shortcut to find what power of 2 = 16
- Prime factorization - until reach ( 1 )
- How many times you divided
16,
8 × 2
4 × 2
2 × 2
2 × 1
( 4 times) so 2⁴