Multiplikation von Potenzen mit gleicher Basis – Lösungen
1. a) 34  35  32
11
=3
e) k3  k5  m2  m7
= k8m9
2. a) x 2  xn
= x2+n
e) a5  a2x
= a2x+5
3. a) x3  xm2
= xm+1
e) a2x  ax 1  a3x 4
= a6x-3
b) 123  125  122
= 1210
f) x5  y3  x 2  y
= x7y4
c) x3  x 2  x
= x6
g) a2  b  b3  a
= a³b4
d) d3  d5  d4
= d12
h) p4  q6  p  q5
= p5q11
b) bm  b3
= bm+3
f) z2m  zm
= z3m
c) ya  y
= ya+1
g) a3m  a2m  am
= a6m
d) xm  xm
= x2m
h) m3x  m4x  m2x
= m9x
b) a5  ax 7
= ax-2
f) xm2  x3m4  x 2m3
= x6m+1
c) y2m  ym1
= y3m-1
g) zp1  z3p4  z5p8
= z9p-5
d) xp4  xp2
= x2p-2
h) ym2  y2m5  ym8
= y4m+1
4
4. a) 5x²(x³6 + x )
b) a³(a5 + a4)
= a8 + a7
e) y2a(y3a+1 – ya-4)
= y5a+1 – y3a-4
=x +x
d) am(am+1 – a3m-1)
= a2m+1 – a4m-1
= x + 2x + x6
e) (2a² + 3a³)²
b) (y3 – y4)²
= y6 – 2y7 + y8
f) (4x5 – 2x6)²
= 4a + 12a + 9a
= 16x
5. a) 4(x² + x³)²
5
4
5
6
10
– 16x
11
+ 4x
12
c) 3b³(4b² - 5b5)
= 12b5 – 15b8
f) xn-3(x5 + x4)
= xn+2 + xn+1
c) (a6 + a4)²
= a12 + 2a10 + a8
g) (6d5 – 3d4)²
d) (b3 – b7)²
= b6 – 2b10 + b14
h) (3m² + 5m7)²
– 36d + 9d
= 9m +30m + 25m
= 36d
10
9
b) (x5 + y4)(x5 – y4)
=a –a
= x10 – y8
d) (3x4 – 2y5)(3x4 + 2y5) e) (4y³ - 6x7)(4y³ + 6x7)
= 9x8 – 4y10
= 16y6 – 36x14
6. a) 4(a² +6a³)(a² – a³)
3
4
+ a5)
7. a) 5(a +8 a )(a²
6
9
8
4
9
14
c) (m³ + n5)(m³ - n5)
= m6 – n10
f) (3a4 – 4b³)(3a4 + 4b³)
= 9a8 – 16b6
=a +a +a +a
d) (y4 + y5)(y3 – y6)
b) (x² – x5)(x³ + x6)
= x5 – x11
e) (2a5 + 3b3)(2a3 – 2b4)
c) (a3 – b²)(a5 + b³)
= a8 + a3b3 – a5b² – b5
f) (km + kn)(km+1 + kn+2)
= y7 – y10 + y8 – y11
= 4a8 – 4a5b4 + 6a³b³ – 6b7
= k2m+1+km+n+2+km+n+1+k2n+2
8. Schreibe als Produkt von Potenzen.
a) x3+5
 x3  x5
© mathepower.de
b) a3n+2
 a3n  a2
c) 5m+n
 5m  5n
d) z5k+3m
 z5k  z3m
xm+4
 xm  x 4

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