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# Fasit

## Aktiviteter 1

### 1.1)

a)
${8}^{4}$
b)
${3}^{3}$
c)
${2}^{8}$
d)
${9}^{5}$
e)
$10{0}^{3}$
f)
${6}^{1}=6$

### 1.2)

a)
${2}^{4}$
b)
${4}^{2}$
c)
${2}^{5}$
d)
${3}^{2}$
e)
${9}^{2}$
f)
${3}^{4}$
g)
${5}^{3}$
h)
$1{0}^{3}$
i)
$1{0}^{5}$
j)
$1{1}^{3}$

a)
${2}^{4}$
b)
${4}^{2}$
c)
${2}^{5}$
d)
${3}^{2}$
e)
${9}^{2}$
f)
${3}^{4}$
g)
${5}^{3}$
h)
$1{0}^{3}$
i)
$1{0}^{5}$
j)
$1{1}^{3}$

### 1.3)

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

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

## Aktiviteter 2

### 2.1)

a)
$1000$
b)
$100\phantom{\rule{0.17em}{0ex}}000$
c)
$10$
d)
$100$
e)
$1$
f)
$0,000\phantom{\rule{0.17em}{0ex}}01$
g)
$0,1$
h)
$0,01$
i)
$0,000\phantom{\rule{0.17em}{0ex}}001$

a)
$1000$
b)
$100\phantom{\rule{0.17em}{0ex}}000$
c)
$10$
d)
$100$
e)
$1$
f)
$0,000\phantom{\rule{0.17em}{0ex}}01$
g)
$0,1$
h)
$0,01$
i)
$0,000\phantom{\rule{0.17em}{0ex}}001$

### 2.2)

a)
$200\phantom{\rule{0.17em}{0ex}}000$
b)
$50\phantom{\rule{0.17em}{0ex}}710$
c)
$900\phantom{\rule{0.17em}{0ex}}000$
d)
$356\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}000$
e)
$765,434$
f)
$0,043\phantom{\rule{0.17em}{0ex}}187\phantom{\rule{0.17em}{0ex}}5$
g)
$6235,489\phantom{\rule{0.17em}{0ex}}81$
h)
$5,234$

a)
$200\phantom{\rule{0.17em}{0ex}}000$
b)
$50\phantom{\rule{0.17em}{0ex}}710$
c)
$900\phantom{\rule{0.17em}{0ex}}000$
d)
$356\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}000$
e)
$765,434$
f)
$0,043\phantom{\rule{0.17em}{0ex}}187\phantom{\rule{0.17em}{0ex}}5$
g)
$6235,489\phantom{\rule{0.17em}{0ex}}81$
h)
$5,234$

## Aktiviteter 3

### 3.1)

a)
$8$
b)
$25$
c)
$1000$
d)
$81$
e)
$13$
f)
$17$
g)
$3$
h)
$107$

a)
$8$
b)
$25$
c)
$1000$
d)
$81$
e)
$13$
f)
$17$
g)
$3$
h)
$107$

### 3.2)

a)
$36$
b)
$126$
c)
$1100$
d)
$90$
e)
$36$
f)
$3$
g)
$39$
h)
$90$

a)
$36$
b)
$126$
c)
$1100$
d)
$90$
e)
$36$
f)
$3$
g)
$39$
h)
$90$

### 3.3)

a)
$54$
b)
$4$
c)
$189$
d)
$32$
e)
$9$
f)
$51$

a)
$54$
b)
$4$
c)
$189$
d)
$32$
e)
$9$
f)
$51$

## Aktiviteter 4

### 4.1)

a)
${4}^{8}$
b)
${5}^{5}$
c)
${4}^{22}$
d)
${5}^{9}$
e)
${7}^{5}$
f)
${4}^{6}$

a)
${4}^{8}$
b)
${5}^{5}$
c)
${4}^{22}$
d)
${5}^{9}$
e)
${7}^{5}$
f)
${4}^{6}$

### 4.2)

a)
${4}^{2}$
b)
${5}^{1}=5$
c)
${4}^{-22}$
d)
${5}^{3}$
e)
$7$
f)
${4}^{-6}$

a)
${4}^{2}$
b)
${5}^{1}=5$
c)
${4}^{-22}$
d)
${5}^{3}$
e)
$7$
f)
${4}^{-6}$

## Aktiviteter 5

### 5.1)

a)
${4}^{-2}$
b)
${4}^{2}$
c)
${6}^{-1}$
d)
${5}^{3}$
e)
$1{2}^{-2}$

a)
${4}^{-2}$
b)
${4}^{2}$
c)
${6}^{-1}$
d)
${5}^{3}$
e)
$1{2}^{-2}$

### 5.2)

a)
${4}^{8}$
b)
${4}^{-22}$
c)
$6$
d)
${5}^{-7}$
e)
$1{2}^{10}$

a)
${4}^{8}$
b)
${4}^{-22}$
c)
$6$
d)
${5}^{-7}$
e)
$1{2}^{10}$

## Aktiviteter 6

### 6.1)

a)
${x}^{13}{y}^{3}$
b)
${a}^{3}{b}^{4}{c}^{5}$
c)
${6}^{3}{t}^{2}$

a)
${x}^{13}{y}^{3}$
b)
${a}^{3}{b}^{4}{c}^{5}$
c)
${6}^{3}{t}^{2}$

### 6.2)

a)
${x}^{4}{y}^{4}$
b)
$64{x}^{2}$
c)
$4{x}^{2}{y}^{2}$
d)
$27{x}^{8}{y}^{5}$
e)
$1{0}^{12}{x}^{4}$
f)
${a}^{6}{b}^{4}$

a)
${x}^{4}{y}^{4}$
b)
$64{x}^{2}$
c)
$4{x}^{2}{y}^{2}$
d)
$27{x}^{8}{y}^{5}$
e)
$1{0}^{12}{x}^{4}$
f)
${a}^{6}{b}^{4}$

### 6.3)

a)
${x}^{18}$
b)
${2}^{4}=16$
c)
$25{x}^{6}$
d)
$32{a}^{15}$
e)
$x$

a)
${x}^{18}$
b)
${2}^{4}=16$
c)
$25{x}^{6}$
d)
$32{a}^{15}$
e)
$x$

### 6.4)

a)
${5}^{0}=1$
b)
${x}^{2}$
c)
${b}^{4}$

a)
${5}^{0}=1$
b)
${x}^{2}$
c)
${b}^{4}$

### 6.5)

a)
$\frac{{y}^{2}}{64{x}^{2}}$
b)
$\frac{2}{{x}^{11}}$
c)
$\frac{{x}^{8}}{4{y}^{8}}$
d)
$270{x}^{2}{y}^{30}$

a)
$\frac{{y}^{2}}{64{x}^{2}}$
b)
$\frac{2}{{x}^{11}}$
c)
$\frac{{x}^{8}}{4{y}^{8}}$
d)
$270{x}^{2}{y}^{30}$

### 6.6)

a)
${3}^{2n}$
b)
${5}^{2}=25$
c)
${4}^{3+x}$

a)
${3}^{2n}$
b)
${5}^{2}=25$
c)
${4}^{3+x}$

## Aktiviteter 7

### 7.1)

a)
$12$
b)
${x}^{5}$
c)
$2×{3}^{-8}$
d)
$c$

a)
$12$
b)
${x}^{5}$
c)
$2×{3}^{-8}$
d)
$c$

### 7.2)

a)
${a}^{4}$
b)
${a}^{3}{b}^{3}$
c)
${a}^{5}b$
d)
${a}^{5}$
e)
${a}^{6}$
f)
${a}^{14}$
g)
${a}^{6}{b}^{6}$
h)
$27a$

a)
${a}^{4}$
b)
${a}^{3}{b}^{3}$
c)
${a}^{5}b$
d)
${a}^{5}$
e)
${a}^{6}$
f)
${a}^{14}$
g)
${a}^{6}{b}^{6}$
h)
$27a$

### 7.3)

a)
${x}^{6}{y}^{-6}$
b)
$\frac{1}{27}$
c)
$\frac{25{x}^{2}}{4}$
d)
$\frac{27{x}^{3}}{8{y}^{3}}$
e)
$\frac{4}{49}$
f)
$\frac{1}{64{a}^{3}}$
g)
$\frac{16{q}^{4}}{81{p}^{4}}$
h)
$\frac{625}{10\phantom{\rule{0.17em}{0ex}}000}$

a)
${x}^{6}{y}^{-6}$
b)
$\frac{1}{27}$
c)
$\frac{25{x}^{2}}{4}$
d)
$\frac{27{x}^{3}}{8{y}^{3}}$
e)
$\frac{4}{49}$
f)
$\frac{1}{64{a}^{3}}$
g)
$\frac{16{q}^{4}}{81{p}^{4}}$
h)
$\frac{625}{10\phantom{\rule{0.17em}{0ex}}000}$

### 7.4)

a)
$\frac{{x}^{12}}{8{y}^{15}}$
b)
$3xy$
c)
$\frac{1}{y}$
d)
$\frac{3{x}^{4}}{{n}^{3}{b}^{9}}$

a)
$\frac{{x}^{12}}{8{y}^{15}}$
b)
$3xy$
c)
$\frac{1}{y}$
d)
$\frac{3{x}^{4}}{{n}^{3}{b}^{9}}$

### 7.5)

a)
${4}^{11}$
b)
$\frac{9}{4{x}^{2}}$
c)
$27{a}^{3}$
d)
$4d$
e)
$\frac{81{k}^{2}}{16}$

a)
${4}^{11}$
b)
$\frac{9}{4{x}^{2}}$
c)
$27{a}^{3}$
d)
$4d$
e)
$\frac{81{k}^{2}}{16}$

### 7.6)

a)
$2{x}^{3}{y}^{2}$
b)
$\frac{{x}^{8}{y}^{8}}{4}$
c)
$270{x}^{2}{y}^{6}$
d)
$\frac{4}{125x}$
e)
$36a$
f)
$\frac{{c}^{9}x}{8{a}^{4}{b}^{2}}$

a)
$2{x}^{3}{y}^{2}$
b)
$\frac{{x}^{8}{y}^{8}}{4}$
c)
$270{x}^{2}{y}^{6}$
d)
$\frac{4}{125x}$
e)
$36a$
f)
$\frac{{c}^{9}x}{8{a}^{4}{b}^{2}}$

### 7.7)

a)
${6}^{x-y}$
b)
${7}^{7-cd}$
c)
${5}^{k+b}{x}^{k-2b}$

a)
${6}^{x-y}$
b)
${7}^{7-cd}$
c)
${5}^{k+b}{x}^{k-2b}$

## Aktiviteter 8

### 8.1)

a)
${a}^{\frac{7}{6}}=\sqrt[6]{{a}^{7}}$
b)
${b}^{\frac{13}{15}}=\sqrt[15]{{b}^{13}}$
c)
${c}^{\frac{1}{2}}=\sqrt{c}$
d)
${d}^{\frac{1}{21}}=\sqrt[21]{d}$
e)
${e}^{\frac{13x}{9y}}=\sqrt[9y]{{e}^{13x}}$
f)
${k}^{\frac{11}{15}}=\sqrt[15]{{k}^{11}}$

a)
${a}^{\frac{7}{6}}=\sqrt[6]{{a}^{7}}$
b)
${b}^{\frac{13}{15}}=\sqrt[15]{{b}^{13}}$
c)
${c}^{\frac{1}{2}}=\sqrt{c}$
d)
${d}^{\frac{1}{21}}=\sqrt[21]{d}$
e)
${e}^{\frac{13x}{9y}}=\sqrt[9y]{{e}^{13x}}$
f)
${k}^{\frac{11}{15}}=\sqrt[15]{{k}^{11}}$

### 8.2)

a)
${a}^{3}$
b)
${a}^{2}$
c)
$\sqrt[15]{{a}^{29}}$

## Aktiviteter 9

### 9.1)

a)
$\frac{1}{\sqrt{2}}$
b)
${2}^{-\frac{3}{2}}$
c)
$3$

### 9.2)

a)
$\sqrt{b}$
b)
$\frac{\sqrt[3]{a}}{{b}^{2}}$
c)
$\frac{{y}^{2}}{x}$

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