Hovedemner i matte

# Aktiviteter 6

### 6.1)

Forenkle uttrykkene så mye som mulig.

a)
${x}^{8}\cdot {y}^{2}\cdot {x}^{4}\cdot x\cdot y$
b)
$a\cdot b\cdot c\cdot {a}^{2}\cdot {b}^{3}\cdot {c}^{4}$
c)
${6}^{2}\cdot {t}^{3}\cdot 6\cdot {t}^{-1}$

### 6.2)

Forenkle uttrykkene så mye som mulig.

a)
${\left(x\cdot y\right)}^{4}$
b)
${\left(8x\right)}^{2}$
c)
${\left(2xy\right)}^{2}$
d)
${\left(xy\right)}^{5}{\left(3x\right)}^{3}$
e)
$\phantom{\rule{-0.17em}{0ex}}{\left(1{0}^{3}x\right)}^{4}$
f)
$\phantom{\rule{-0.17em}{0ex}}{\left(a\cdot {b}^{2}\right)}^{2}\cdot {a}^{4}$

a)
${\left(x\cdot y\right)}^{4}$
b)
${\left(8x\right)}^{2}$
c)
${\left(2xy\right)}^{2}$
d)
${\left(xy\right)}^{5}{\left(3x\right)}^{3}$
e)
$\phantom{\rule{-0.17em}{0ex}}{\left(1{0}^{3}x\right)}^{4}$
f)
$\phantom{\rule{-0.17em}{0ex}}{\left(a\cdot {b}^{2}\right)}^{2}\cdot {a}^{4}$

### 6.3)

Forenkle uttrykkene så mye som mulig.

a)
$\phantom{\rule{-0.17em}{0ex}}{\left({x}^{3}\right)}^{6}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left({2}^{2}\right)}^{2}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(5{x}^{3}\right)}^{2}$
d)
$\phantom{\rule{-0.17em}{0ex}}{\left(2{a}^{3}\right)}^{5}$
e)
${x}^{2}\cdot {x}^{-1}$

a)
$\phantom{\rule{-0.17em}{0ex}}{\left({x}^{3}\right)}^{6}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left({2}^{2}\right)}^{2}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(5{x}^{3}\right)}^{2}$
d)
$\phantom{\rule{-0.17em}{0ex}}{\left(2{a}^{3}\right)}^{5}$
e)
${x}^{2}\cdot {x}^{-1}$

### 6.4)

Regn ut om mulig eller skriv svaret som én potens.

a)
${5}^{-6}×{5}^{8}×{5}^{-2}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left({x}^{-2}\right)}^{-1}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(\phantom{\rule{-0.17em}{0ex}}{\left({b}^{2}\right)}^{-1}\right)}^{-2}$

### 6.5)

Forenkle uttrykkene så mye som mulig.

a)
$\phantom{\rule{-0.17em}{0ex}}{\left(8x{y}^{-1}\right)}^{-2}$
b)
$32x\cdot \phantom{\rule{-0.17em}{0ex}}{\left(2{x}^{3}\right)}^{-4}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(8x{y}^{4}\right)}^{-2}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(4{x}^{5}\right)}^{2}$
d)
$\phantom{\rule{-0.17em}{0ex}}{\left(3{y}^{6}\right)}^{3}\cdot 10{x}^{2}{y}^{12}$

a)
$\phantom{\rule{-0.17em}{0ex}}{\left(8x{y}^{-1}\right)}^{-2}$
b)
$32x\cdot \phantom{\rule{-0.17em}{0ex}}{\left(2{x}^{3}\right)}^{-4}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(8x{y}^{4}\right)}^{-2}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(4{x}^{5}\right)}^{2}$
d)
$\phantom{\rule{-0.17em}{0ex}}{\left(3{y}^{6}\right)}^{3}\cdot 10{x}^{2}{y}^{12}$

### 6.6)

Skriv så enkelt som mulig.

a)
${3}^{n}\cdot {3}^{n}$
b)
${5}^{n}\cdot {5}^{1-n}\cdot 5$
c)
${4}^{3}\cdot {4}^{x}$
d)
${\left(5x\right)}^{k}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(5{x}^{-2}\right)}^{b}$

a)
${3}^{n}\cdot {3}^{n}$
b)
${5}^{n}\cdot {5}^{1-n}\cdot 5$
c)
${4}^{3}\cdot {4}^{x}$
d)
${\left(5x\right)}^{k}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(5{x}^{-2}\right)}^{b}$

Du kan finne fasit her.

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