Activities 6

6.1)

Simplify the expressions as much as possible:

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)

Simplify the expressions as much as possible:

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)

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)
${x}^{2}\cdot {x}^{-1}$

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)

Calculate if possible or write as a single power:

a)
${5}^{-6}\cdot {5}^{8}\cdot {5}^{-2}$
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)
$32x\cdot \phantom{\rule{-0.17em}{0ex}}{\left(2{x}^{3}\right)}^{-4}$
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)

Simplify as much as possible:

a)
${3}^{n}\cdot {3}^{n}$
b)
${5}^{n}\cdot {5}^{1-n}\cdot 5$
c)
${4}^{3}\cdot {4}^{x}$

a)
${3}^{n}\cdot {3}^{n}$
b)
${5}^{n}\cdot {5}^{1-n}\cdot 5$
c)
${4}^{3}\cdot {4}^{x}$

You can find the solutions here.