Conclude as far as possible.
a3:a6
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
First Representation
a⋅a⋅a⋅a⋅a⋅aa⋅a⋅a = ↓ Shorten by cancelling three factors of a.
= a⋅a⋅a1 = a31=a−3 Second Representation
a3:a6 = ↓ Apply the power laws.
= a3−6 = a−3 Do you have a question?
2x−2⋅3x3
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
Power laws
2x−2⋅3x3 = ↓ Use the commutative law to group numbers and variables together.
= 2⋅3⋅x−2⋅x3 ↓ Apply the power laws.
= 2⋅3⋅x−2+3 = 6x Do you have a question?
10−12:10−3
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
Power laws
10−12:10−3 = ↓ Apply the power laws.
= 10−12−(−3) = 10−9 Do you have a question?
6:23−9⋅3−2
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
6:23−9⋅3−2 = ↓ Write 9 as 32.
= 6:23−32⋅3−2 ↓ Apply the power laws.
= 6:8−32+(−2) = 6:8−30 = 0.75−1 = −0.25 Do you have a question?
x−n⋅x
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
x−n⋅x = ↓ Write x as x1.
= x−n⋅x1 ↓ Apply the power laws.
= x−n+1 Alternative solution
x−n⋅x = ↓ Write x−n as xn1.
= xn1⋅x1 = xnx1 ↓ Apply the power laws.
= x1−n Do you have a question?
0.5x2+1.5x3
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
This term cannot be simplified further, since two different powers occur. However, what one could do is factorizing the term:
0.5x2+1.5x3 = ↓ Factorize 0.5x2.
= 0.5x2(1+3x) Do you have a question?
(y−5y2x3y−4)−2
Für diese Aufgabe benötigst Du folgendes Grundwissen: Powers
First apply the power laws. You may get the minus out of the exponent by "flipping" the fractions like x−2=x21.
(y−5y2x3y−4)−2 = (x3y−4y−5y2)2 ↓ Apply the power laws.
= (x3y−4y−5+2)2 = (x3y−4y−3)2 ↓ Shorten by y−3.
= (x3y−11)2 ↓ Apply the power laws once more.
= (x3y)2 = x6y2 Do you have a question?
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