2.03 Division properties of exponents and the zero exponent
Simplify the following, giving your answers in exponential form.
10^{8} \div 10^{6}
j^{8} \div j^{4}
a^{5} \div a^{3}
9 q^{6} \div \left( 4 q^{2}\right)
Simplify the following, giving your answers with positive exponents.
\dfrac{18^{32}}{18^{23}}
\dfrac{a^{10}}{a^{6}}
\dfrac{u^{13}}{u^{2}}
\dfrac{t^{7} r^{8}}{t^{5} r^{4}}
\dfrac{5 r^{7}}{r^{4}}
\dfrac{3 j^{13}}{4 j^{8}}
\dfrac{- x^{11}}{3 x^{4}}
\dfrac{9 j^{9} k^{8}}{4 j^{7}}
\dfrac{3 g^{8}}{2 g^{5} h^{6}}
\dfrac{9 j^{5} k^{7}}{j^{3} k^{4}}
\dfrac{j^{8} k^{9}}{7 j^{7} k^{8}}
\dfrac{3 m^{9} n^{4}}{8 m^{8} n^{2}}
\dfrac{4 p^{3} q^{9}}{2 p^{2} q^{7}}
\dfrac{2 p^{9} q^{6}}{6 p^{3} q^{3}}
\dfrac{3 j^{6} k^{4}}{2 j^{4} k^{2}}
\dfrac{y^{6}}{\left( 4 y\right)^{2}}
\dfrac{6 r^{3} s^{6}}{2 r^{2} s^{4}}
\dfrac{- 9 x^{13}}{3 x^{4}}
\dfrac{x^{6}}{4 x^{4}}
\dfrac{54 x^{11}}{6 x^{6}}
For the following, write the integer value or the term that should go in the space.
a^{9} \div a^{⬚} = a^{7}
15 j^{14} \div \left(⬚\right) = 5 j^{7}
x^{23} y^{10} \div \left(⬚\right) = x^{15} y^{5}
⬚ \div \left( g^{4} h^{3}\right) = g^{16} h^{5}
63 x^{18} \div ⬚ = 9 x^{14}
x^{21} y^{8} \div ⬚ = x^{14} y^{3}
\dfrac{8 r^{3} s^{8}}{⬚} = 2 r s^{2}
Simplify the following, giving your answers in exponential form:
\dfrac{\left( n^{8} r^{5}\right)^{5}}{\left( n^{4} r\right)^{5}}
\dfrac{30 x^{13} y^{26} z^{21}}{3 x^{11} y^{15} z^{6}}
\dfrac{15 x^{16} y^{25} z^{13}}{- 3 x^{14} y^{11} z^{2}}
\left(m^{12}\right)^{9} \div \left(m^{4}\right)^{2}
\left( - 240 u^{32} \right) \div \left( - 8 u^{9}\right) \div \left( - 5 u^{12} \right)
\dfrac{y^{7} \cdot y^{5}}{y^{3} \cdot y^{2}}
\dfrac{10 p^{6} \cdot 3 p^{10}}{15 p^{2}}
\dfrac{\left( 2 x^{4} y^{0}\right)^{2}}{x^{6}}
\dfrac{6 \left( w^{2} v\right)^{5} \cdot 27 y^{17} v^{7}}{\left( 3 w^{5} v^{3}\right)^{2} \cdot 2 y^{6} v}
m^{9} \div m^{5} \cdot m^{4}
p^{18} \div p^{8} \div p^{5}
\dfrac{\left(x^{3}\right)^{2}}{x^{3}}
\dfrac{45 b^{6}}{\left( 3 b\right) \left( 5 a\right)}
\dfrac{210 p^{22}}{7 p^{8}} \div \left( 5 p^{7}\right)
Fill in the missing value to complete the pattern.
| k^5 = 1 \cdot k \cdot k \cdot k \cdot k \cdot k |
| k^4 = 1 \cdot k \cdot k \cdot k \cdot k |
| k^3 = 1 \cdot k \cdot k \cdot k |
| k^2 = 1 \cdot k \cdot k |
| k^1 = 1 \cdot k |
| k^0 = ⬚ |
Fill in the missing exponent to make the following equations true.
p^{12} \div p^{12} = p^{⬚}
\dfrac{b^{⬚}}{b^{11}} = b^{0}
\dfrac{w^{7}}{w^{⬚}} = w^{0}
Evaluate:
741^{0}
\left( - 983 \right)^{0}
\left( 2 \cdot 13\right)^{0}
Simplify:
18 a^{0}
q^{0}
11 a^{0}
\left( 6 a\right)^{0}
\left(a^{0}\right)^{79}
9 \cdot \left( 15 x^{6}\right)^{0}
\left( 3 m^{4}\right)^{3} \cdot m q^{0}
\dfrac{45 x^{7} y^{7}}{9 x^{7} y^{2}}
When simplifying the expression \dfrac{a^5\cdot a^4}{a^2}, Chad's first line of work was a^3\cdot a^2.
Is Chad's work correct? Explain.
When simplifying the expression \dfrac{a^5+a^4}{a^2}, Clarice's first line of work was a^3+a^2.
Is Clarice's work correct? Explain.