2.04 Negative exponents
Express the following using only positive exponents:
p^{ - 2 }
a^{ - 8 }
3 x^{ - 2 }
10 x^{ - 6 }
4 a^{ - 2 }
4 y^{ - 3 }
\dfrac{1}{a^{ - n }}
\dfrac{a^{ - n }}{b^{ - m }}
p^{ - 2 } q^{3}
8 p^{ - 3 }
m^{ - 5 } n^{ - 4 } p^{4}
Express the following using only negative exponents:
\dfrac{1}{u^{5}}
\dfrac{10}{p^{8} q^{5}}
Write an expression for the reciprocal of a^{3}.
Find the value of n on the following equations:
\dfrac{1}{36} = 6^{n}
\dfrac{1}{8} = 2^{n}
Determine the missing exponent so that following equation is always true.
\left( a^{3} b^{ - 5 }\right)^{⬚} = a^{ - 15 } b^{25}
Simplify the following, expressing your answers using positive exponents:
4 y^{ - 5 } \cdot 3 y^{ - 3 }
\left( 6 m\right)^{2} \cdot m^{ - 6 }
2 y^{3} \cdot \left( - 2 y^{ - 7 } \right)
6 y^{7} \cdot 2 y^{ - 5 } \cdot 5 y^{3}
5 p^{3} q^{ - 2 } \cdot 9 p^{ - 3 } q^{5}
5 p^{7} q^{ - 7 } \cdot 5 p^{ - 7 } q^{3}
8 p^{5} q^{ - 5 } \cdot 4 p^{ - 4 } q^{3}
2 p^{4} q^{ - 2 } \cdot 5 p^{ - 4 } q^{ - 5 }
5 p^{ - 6 } q^{ - 9 } \cdot \left( - 6 p^{ - 4 } q^{ - 3 }\right)
\left(w^{4}\right)^{ - 5 }
\left(w^{ - 9 }\right)^{5}
\left(5^{2}\right)^{ - p }
\left( 4 y^{4}\right)^{ - 4 }
\left( 2 y^{ - 5 }\right)^{4}
\left( - 4 u^{ - 4 } \right)^{3}
\left( - u^{3} \right)^{ - 4 }
\left( 4 m^{ - 10 }\right)^{4}
\left( 4 m^{ - 8 }\right)^{ - 3 }
\left( 4 m\right)^{ - 3 }
\left( 5 y^{3}\right)^{ - 3 }
\left( 4 p^{8} q^{4}\right)^{ - 2 }
\left( \dfrac{4}{5} u^{ - 3 }\right)^{4}
\left(\dfrac{y}{2}\right)^{ - 5 }
Assuming that all variables are non-zero, simplify the following. Express your answers using positive exponents.
\dfrac{12 x^{3}}{4 x^{7}}
\dfrac{6 x^{3}}{2 x^{ - 3 }}
\dfrac{25 x^{ - 7 }}{5 x^{ - 4 }}
\left(\dfrac{a}{b}\right)^{ - 5 }
\left(\dfrac{a^{3}}{b^{3}}\right)^{ - 5 }
\left(\dfrac{a^{2}}{b^{5}}\right)^{ - 1 }
\left(\dfrac{3 a^{9}}{b^{9}}\right)^{ - 2 }
\dfrac{- 4 x^{2}}{2 x^{ - 5 }}
\dfrac{- 6 x^{ - 7 }}{- 2 x^{ - 4 }}
\dfrac{z^{ - 2 } x^{ - 5 }}{y^{ - 7 }}
\dfrac{\left( 6 y^{3} z^{2}\right)^{ - 4 }}{\left( 6 y^{3} z^{2}\right)^{ - 5 }}
\dfrac{5 p^{5} q^{ - 4 }}{40 p^{5} q^{6}}
\left(\dfrac{2 y^{3} x^{0}}{z^{2}}\right)^{ - 4 }
\dfrac{x^{2} y^{ - 3 }}{x^{ - 5 } y^{2}}
\dfrac{\left(m^{ - 3 }\right)^{ - 1 } \cdot \left(m^{4}\right)^{ - 3 }}{m^{3} \cdot m^{4}}
\left(\dfrac{m^{7}}{m^{ - 10 }}\right)^{2} \cdot \left(\dfrac{m^{5}}{m^{2}}\right)^{ - 3 }
\dfrac{a^{2} \cdot a^{ - 5 } \cdot b^{ - 2 }}{\left( a \cdot a^{ - 5 } \cdot b^{2}\right)^{2}}