Is 2^{ - 3 } less than or greater than 1?
Express the following with positive exponents:
a^{ - 9 }
\dfrac{1}{a^{ - n }}
\dfrac{a^{ - 9 }}{4}
\dfrac{a^{ - n }}{b^{ - m }}
p^{ - 2 }
3 x^{ - 4 }
7 x^{ - 9 }
p^{-2}q^3
8p^{-3}
2x^{-8}y^3
Express the following without fractions:
Simplify the following, giving your answers with positive exponents:
5 y^{9} \times 4 y^{ - 3 }
7 a^{4} \times 4 a^{-2}
5x^4\times \left(-3x^{-8}\right)
3y^{-2}\times 4y^{-3}
2h^{-4}\times 4h^{11}
3y^{-2}\times 2y^{-5}
-4y^2\times \left(-4y^{-5}\right)
\left(5mp\right)^2\times mp^{-2}
\dfrac{9 x^{2}}{3 x^{9}}
\dfrac{15x^3}{5x^7}
Simplify the following, giving your answers with positive exponents:
\left( 2 m\right)^{ - 3 }
\left(4m^{-6}\right)^4
\left(3p^{-4}\right)^{-2}
\left( 3 y^{2}\right)^{ - 2 }
\left(\dfrac{y}{4}\right)^{ - 3 }
\left(\dfrac{x^{5}}{y^{4}}\right)^{ - 1 }
\left(\dfrac{x^{7}}{y^{9}}\right)^{ - 4 }
\dfrac{20 x^{3}}{4 x^{ - 2 }}
\dfrac{10 x^{ - 7 }}{2 x^{ - 3 }}
\left(\dfrac{z}{3}\right)^{ - 4 }
\left(\dfrac{p^{3}}{q^{7}}\right)^{ - 1 }
\left(\dfrac{x^{-4}}{y^{-8}}\right)^{ - 2 }
Solve the following equations for n:
\dfrac{1}{25} = 5^{n}
\dfrac{1}{8} = 2^{n}
\left( x^{3} y^{ - 5 }\right)^{n} = x^{ - 12 } y^{20}
\left( a^{-5} b^{ 3 }\right)^{n} = a^{ 15 } b^{-9}
Complete the following:
\left(x^4 y^⬚\right)^⬚=\dfrac{y^{12}}{x^{16}}A student was writing 5a^{-1} without negative exponents and wrote 5a^{-1}=\dfrac{1}{5a}. Explain why their working is incorrect, and write the correct answer.
Simplify:
2 y^{6} \times 4 y^{7} \times 4 y^{ - 5 }
6 y^{7} \times 2 y^{ - 5 } \times 5 y^{3}
Simplify the following, giving your answers with positive exponents: