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>Powers>Activities 7

At the bottom of the page there is an interactive quiz.

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): $\frac{\frac{2^{3}}{3^{3}}}{\frac{3^{5}}{2^{- 2}}}$
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): $\frac{\frac{2^{3}}{3^{3}}}{\frac{3^{5}}{2^{- 2}}}$
d): $\frac{c}{c^{2} \cdot c^{- 3} \cdot c}$

7.2)

Calculate and write as powers if possible:

a): $\frac{a^{2} \cdot {(a^{4})}^{2}}{{(a^{2})}^{3}}$
b): $\frac{a^{2} \cdot b^{6} \cdot a^{5}}{a^{4} \cdot b^{3}}$
c): $\frac{{(a \cdot b)}^{4} \cdot a^{3}}{a^{2} \cdot b^{3}}$
d): $\frac{a^{0} \cdot a^{4} \cdot {(a^{3})}^{2}}{a^{5} \cdot b^{0}}$
e): $\frac{a^{12} \cdot a^{- 3}}{a^{7} \cdot a^{- 4}}$
f): $\frac{a^{3} \cdot {(a^{- 2})}^{- 3}}{a^{- 5}}$
g): $\frac{{(a \cdot b)}^{2} \cdot a^{5}}{a \cdot b^{- 4}}$
h): $\frac{{(3 a)}^{3} \cdot {(a^{- 2})}^{2}}{a^{- 2}}$

7.3)

Simplify as much as possible:

a): ${(\frac{x}{y})}^{6}$
b): ${(\frac{1}{3})}^{3}$
c): ${(\frac{5 x}{2})}^{2}$
d): ${(\frac{3 x}{2 y})}^{3}$
e): ${(\frac{2}{7})}^{2}$
f): ${(\frac{1}{4 a})}^{3}$
g): ${(\frac{2 g}{3 p})}^{4}$
h): ${(\frac{5}{10})}^{4}$

a): ${(\frac{x}{y})}^{6}$
b): ${(\frac{1}{3})}^{3}$
c): ${(\frac{5 x}{2})}^{2}$
d): ${(\frac{3 x}{2 y})}^{3}$
e): ${(\frac{2}{7})}^{2}$
f): ${(\frac{1}{4 a})}^{3}$
g): ${(\frac{2 g}{3 p})}^{4}$
h): ${(\frac{5}{10})}^{4}$

7.4)

Simplify as much as possible:

a): ${(\frac{x^{4}}{2 y^{5}})}^{3}$
b): $x^{2} \cdot \frac{3 y}{x}$
c): $\frac{\frac{x^{4}}{y^{7}}}{{(\frac{x^{2}}{y^{3}})}^{2}}$
d): $\frac{1}{12 n^{3}} \cdot \frac{{(6 x^{2})}^{2}}{b^{9}}$

7.5)

Simplify as much as possible:

a): $\frac{4^{5}}{4^{- 6}}$
b): ${(\frac{2 x}{3})}^{- 2}$
c): $\frac{{(3 a)}^{3}}{1^{- 2}}$
d): $\frac{d}{{(- 2)}^{- 2}}$
e): ${(\frac{4^{2}}{{(9 k)}^{2}})}^{- 1}$

a): $\frac{4^{5}}{4^{- 6}}$
b): ${(\frac{2 x}{3})}^{- 2}$
c): $\frac{{(3 a)}^{3}}{1^{- 2}}$
d): $\frac{d}{{(- 2)}^{- 2}}$
e): ${(\frac{4^{2}}{{(9 k)}^{2}})}^{- 1}$

7.6)

Simplify as much as possible:

a): $\frac{6 x^{5} {(x y^{2})}^{- 1}}{3 x y^{- 4}}$
b): ${(\frac{8 x}{y^{4}})}^{- 2} \cdot {(4 x^{5})}^{2}$
c): ${(3 y^{6})}^{3} \cdot \frac{10 x^{2}}{y^{12}}$
d): $5 \cdot \frac{4 x^{3}}{{(5 x)}^{4}}$
e): $\frac{{(6 x)}^{4}}{9 a^{5}} \cdot \frac{{(3 a^{3})}^{2}}{36 x^{4}}$
f): $\frac{8^{- 1} a {(b c^{3})}^{3} x}{{(a b)}^{5}}$

7.7)

Simplify as much as possible:

a): $\frac{6^{x}}{6^{y}}$
b): $\frac{7^{4} \cdot 7^{3}}{7^{c d}}$
c): ${(5 x)}^{k} \cdot {(\frac{5}{x^{2}})}^{b}$

a): $\frac{6^{x}}{6^{y}}$
b): $\frac{7^{4} \cdot 7^{3}}{7^{c d}}$
c): ${(5 x)}^{k} \cdot {(\frac{5}{x^{2}})}^{b}$

You can find the solutions here.

Example with Fractions

Example with Roots