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### Section 1-1 : Integer Exponents

For problems 1 – 10 evaluate the given expression and write the answer as a single number with no exponents.

1. $$2 \cdot {5^2} + {\left( { - 4} \right)^2}$$
2. $${6^0} - {3^5}$$
3. $$3 \cdot {4^3} + 2 \cdot {3^2}$$
4. $${\left( { - 1} \right)^4} + 2{\left( { - 3} \right)^4}$$
5. $${7^0}{\left( {{4^2} \cdot {3^2}} \right)^2}$$
6. $$- {4^3} + {\left( { - 4} \right)^3}$$
7. $$8 \cdot {2^{ - 3}} + {16^0}$$
8. $${\left( {{2^{ - 1}} + {3^{ - 1}}} \right)^{ - 1}}$$
9. $$\displaystyle \frac{{{3^2} \cdot {{\left( { - 2} \right)}^3}}}{{{6^{ - 2}}}}$$
10. $$\displaystyle \frac{{{4^{ - 2}} \cdot {5^3}}}{{{3^{ - 4}}}}$$

For problems 11 – 18 simplify the given expression and write the answer with only positive exponents.

1. $${\left( {3{x^{ - 2}}{y^{ - 4}}} \right)^{ - 1}}$$
2. $${\left( {{{\left( {2{a^2}} \right)}^{ - 3}}{b^4}} \right)^{ - 3}}$$
3. $$\displaystyle \frac{{{c^{ - 6}}{b^{10}}}}{{{b^9}{c^{ - 11}}}}$$
4. $$\displaystyle \frac{{4{a^3}{{\left( {{b^2}a} \right)}^{ - 4}}}}{{{c^{ - 6}}{a^2}{b^{ - 7}}}}$$
5. $$\displaystyle \frac{{{{\left( {6{v^2}} \right)}^{ - 1}}{w^{ - 4}}}}{{{{\left( {2v} \right)}^{ - 3}}{w^{10}}}}$$
6. $${\left( \frac{{{{\left( {8{x^{21}}} \right)}^0}{y^{ - 3}}{x^8}}}{{{y^{ - 9}}{x^{ - 1}}}}} \right)^6$$
7. $${\left( \frac{{{a^2}{b^{ - 4}}{c^{ - 1}}}}{{{b^{ - 9}}{c^8}{a^{ - 4}}}}} \right)^{ - 2}$$
8. $${\left( \frac{{{p^{ - 6}}{q^7}{{\left( {{p^2}q} \right)}^{ - 3}}}}{{{{\left( {{p^{ - 1}}{q^{ - 4}}} \right)}^2}{p^{10}}}}} \right)^3$$

For problems 19 – 23 determine if the statement is true or false. If it is false explain why it is false and give a corrected version of the statement.

1. $$\displaystyle \frac{1}{{6x}} = 6{x^{ - 1}}$$
2. $${\left( {{x^3}} \right)^7} = {x^{10}}$$
3. $${\left( {{m^3}{n^4}} \right)^2} = {m^{12}}{n^8}$$
4. $${\left( {{{\left( {{z^2}} \right)}^3}} \right)^4} = {z^{24}}$$
5. $${\left( {x + y} \right)^3} = {x^3} + {y^3}$$