 # Activities 6

## 6.1)

Simplify the expressions as much as possible:

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

## 6.2)

Simplify the expressions as much as possible:

a)
${\left(x×y\right)}^{4}$
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)
$\phantom{\rule{-0.17em}{0ex}}{\left(a×{b}^{2}\right)}^{2}×{a}^{4}$

a)
${\left(x×y\right)}^{4}$
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)
$\phantom{\rule{-0.17em}{0ex}}{\left(a×{b}^{2}\right)}^{2}×{a}^{4}$

## 6.3)

Simplify the expressions as much as possible:

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)
${x}^{2}×{x}^{-1}$

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)
${x}^{2}×{x}^{-1}$

## 6.4)

Calculate if possible or write as a single power:

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)

Simplify as much as possible:

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

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

## 6.6)

Simplify as much as possible:

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

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

You can find the solutions here.