# Activities 7

## 7.1)

Calculate and write as power(s):

a)
$\frac{1{2}^{15}}{1{2}^{14}}$
b)
$\frac{{x}^{7}\cdot {x}^{4}}{x\cdot {x}^{2}\cdot {x}^{3}}$
c)
$\genfrac{}{}{1.0pt}{}{\phantom{\rule{0.17em}{0ex}}\frac{{2}^{3}}{{3}^{3}}\phantom{\rule{0.17em}{0ex}}}{\phantom{\rule{0.17em}{0ex}}\frac{{3}^{5}}{{2}^{-2}}\phantom{\rule{0.17em}{0ex}}}$
d)
$\frac{c}{{c}^{2}\cdot {c}^{-3}\cdot c}$

a)
$\frac{1{2}^{15}}{1{2}^{14}}$
b)
$\frac{{x}^{7}\cdot {x}^{4}}{x\cdot {x}^{2}\cdot {x}^{3}}$
c)
$\genfrac{}{}{1.0pt}{}{\phantom{\rule{0.17em}{0ex}}\frac{{2}^{3}}{{3}^{3}}\phantom{\rule{0.17em}{0ex}}}{\phantom{\rule{0.17em}{0ex}}\frac{{3}^{5}}{{2}^{-2}}\phantom{\rule{0.17em}{0ex}}}$
d)
$\frac{c}{{c}^{2}\cdot {c}^{-3}\cdot c}$

## 7.2)

Calculate and write as powers if possible:

a)
$\frac{{a}^{2}\cdot \phantom{\rule{-0.17em}{0ex}}{\left({a}^{4}\right)}^{2}}{{\left({a}^{2}\right)}^{3}}$
b)
$\frac{{a}^{2}\cdot {b}^{6}\cdot {a}^{5}}{{a}^{4}\cdot {b}^{3}}$
c)
$\frac{{\left(a\cdot b\right)}^{4}\cdot {a}^{3}}{{a}^{2}\cdot {b}^{3}}$
d)
$\frac{{a}^{0}\cdot {a}^{4}\cdot \phantom{\rule{-0.17em}{0ex}}{\left({a}^{3}\right)}^{2}}{{a}^{5}\cdot {b}^{0}}$
e)
$\frac{{a}^{12}\cdot {a}^{-3}}{{a}^{7}\cdot {a}^{-4}}$
f)
$\frac{{a}^{3}\cdot \phantom{\rule{-0.17em}{0ex}}{\left({a}^{-2}\right)}^{-3}}{{a}^{-5}}$
g)
$\frac{{\left(a\cdot b\right)}^{2}\cdot {a}^{5}}{a\cdot {b}^{-4}}$
h)
$\frac{{\left(3a\right)}^{3}\cdot \phantom{\rule{-0.17em}{0ex}}{\left({a}^{-2}\right)}^{2}}{{a}^{-2}}$

## 7.3)

Simplify as much as possible:

a)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{x}{y}\right)}^{6}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{1}{3}\right)}^{3}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{5x}{2}\right)}^{2}$
d)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{3x}{2y}\right)}^{3}$
e)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{2}{7}\right)}^{2}$
f)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{1}{4a}\right)}^{3}$
g)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{2g}{3p}\right)}^{4}$
h)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{5}{10}\right)}^{4}$

a)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{x}{y}\right)}^{6}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{1}{3}\right)}^{3}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{5x}{2}\right)}^{2}$
d)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{3x}{2y}\right)}^{3}$
e)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{2}{7}\right)}^{2}$
f)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{1}{4a}\right)}^{3}$
g)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{2g}{3p}\right)}^{4}$
h)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{5}{10}\right)}^{4}$

## 7.4)

Simplify as much as possible:

a)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{{x}^{4}}{2{y}^{5}}\right)}^{3}$
b)
${x}^{2}\cdot \frac{3y}{x}$
c)
$\genfrac{}{}{1.0pt}{}{\phantom{\rule{0.17em}{0ex}}\frac{{x}^{4}}{{y}^{7}}\phantom{\rule{0.17em}{0ex}}}{\phantom{\rule{0.17em}{0ex}}\phantom{\rule{-0.17em}{0ex}}{\left(\frac{{x}^{2}}{{y}^{3}}\right)}^{2}\phantom{\rule{0.17em}{0ex}}}$
d)
$\frac{1}{12{n}^{3}}\cdot \frac{\phantom{\rule{-0.17em}{0ex}}{\left(6{x}^{2}\right)}^{2}}{{b}^{9}}$

## 7.5)

Simplify as much as possible:

a)
$\frac{{4}^{5}}{{4}^{-6}}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{2x}{3}\right)}^{-2}$
c)
$\frac{{\left(3a\right)}^{3}}{{1}^{-2}}$
d)
$\frac{d}{{\left(-2\right)}^{-2}}$
e)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{{4}^{2}}{{\left(9k\right)}^{2}}\right)}^{-1}$

a)
$\frac{{4}^{5}}{{4}^{-6}}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{2x}{3}\right)}^{-2}$
c)
$\frac{{\left(3a\right)}^{3}}{{1}^{-2}}$
d)
$\frac{d}{{\left(-2\right)}^{-2}}$
e)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{{4}^{2}}{{\left(9k\right)}^{2}}\right)}^{-1}$

## 7.6)

Simplify as much as possible:

a)
$\frac{6{x}^{5}\phantom{\rule{-0.17em}{0ex}}{\left(x{y}^{2}\right)}^{-1}}{3x{y}^{-4}}$
b)
$\phantom{\rule{-0.17em}{0ex}}{\left(\frac{8x}{{y}^{4}}\right)}^{-2}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(4{x}^{5}\right)}^{2}$
c)
$\phantom{\rule{-0.17em}{0ex}}{\left(3{y}^{6}\right)}^{3}\cdot \frac{10{x}^{2}}{{y}^{12}}$
d)
$5\cdot \frac{4{x}^{3}}{{\left(5x\right)}^{4}}$
e)
$\frac{{\left(6x\right)}^{4}}{9{a}^{5}}\cdot \frac{\phantom{\rule{-0.17em}{0ex}}{\left(3{a}^{3}\right)}^{2}}{36{x}^{4}}$
f)
$\frac{{8}^{-1}a\phantom{\rule{-0.17em}{0ex}}{\left(b{c}^{3}\right)}^{3}x}{{\left(ab\right)}^{5}}$

## 7.7)

Simplify as much as possible:

a)
$\frac{{6}^{x}}{{6}^{y}}$
b)
$\frac{{7}^{4}\cdot {7}^{3}}{{7}^{cd}}$
c)
${\left(5x\right)}^{k}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(\frac{5}{{x}^{2}}\right)}^{b}$

a)
$\frac{{6}^{x}}{{6}^{y}}$
b)
$\frac{{7}^{4}\cdot {7}^{3}}{{7}^{cd}}$
c)
${\left(5x\right)}^{k}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(\frac{5}{{x}^{2}}\right)}^{b}$

You can find the solutions here.