properties of exponents\nsimplify. your answer should contain only positive exponents.\n1)…

properties of exponents\nsimplify. your answer should contain only positive exponents.\n1) $2m^{2}cdot2m^{3}$\n2) $m^{4}cdot2m^{-3}$\n3) $4r^{-3}cdot2r^{2}$\n4) $4n^{4}cdot2n^{-3}$\n5) $2k^{4}cdot4k$\n6) $2x^{3}y^{-3}cdot2x^{-1}y^{3}$\n7) $2y^{2}cdot3x$\n8) $4v^{3}cdot vu^{2}$\n9) $4a^{3}b^{2}cdot3a^{-4}b^{-3}$\n10) $x^{2}y^{-4}cdot x^{3}y^{2}$\n11) $(x^{2})^{0}$\n12) $(2x^{2})^{-4}$\n13) $(4r^{0})^{4}$\n14) $(4a^{3})^{2}$\n15) $(3k^{4})^{4}$\n16) $(4xy)^{-1}$

properties of exponents\nsimplify. your answer should contain only positive exponents.\n1) $2m^{2}cdot2m^{3}$\n2) $m^{4}cdot2m^{-3}$\n3) $4r^{-3}cdot2r^{2}$\n4) $4n^{4}cdot2n^{-3}$\n5) $2k^{4}cdot4k$\n6) $2x^{3}y^{-3}cdot2x^{-1}y^{3}$\n7) $2y^{2}cdot3x$\n8) $4v^{3}cdot vu^{2}$\n9) $4a^{3}b^{2}cdot3a^{-4}b^{-3}$\n10) $x^{2}y^{-4}cdot x^{3}y^{2}$\n11) $(x^{2})^{0}$\n12) $(2x^{2})^{-4}$\n13) $(4r^{0})^{4}$\n14) $(4a^{3})^{2}$\n15) $(3k^{4})^{4}$\n16) $(4xy)^{-1}$

Answer

Explanation:

Step1: Use product - rule of exponents (a^m\cdot a^n=a^{m + n}) and (c\cdot a^m\cdot d\cdot a^n=(c\cdot d)a^{m + n})

  1. For (2m^{2}\cdot2m^{3}), we have ((2\times2)m^{2 + 3}=4m^{5})
  2. For (m^{4}\cdot2m^{-3}), we get (2m^{4+( - 3)}=2m^{1}=2m)
  3. For (4r^{-3}\cdot2r^{2}), it is ((4\times2)r^{-3 + 2}=8r^{-1}=\frac{8}{r})
  4. For (4n^{4}\cdot2n^{-3}), we have ((4\times2)n^{4+( - 3)}=8n^{1}=8n)
  5. For (2k^{4}\cdot4k), we get ((2\times4)k^{4 + 1}=8k^{5})
  6. For (2x^{3}y^{-3}\cdot2x^{-1}y^{3}), we have ((2\times2)x^{3+( - 1)}y^{-3 + 3}=4x^{2}y^{0}=4x^{2})
  7. For (2y^{2}\cdot3x), it is ((2\times3)xy^{2}=6xy^{2})
  8. For (4v^{3}\cdot vu^{2}), we get (4v^{3 + 1}u^{2}=4v^{4}u^{2})
  9. For (4a^{3}b^{2}\cdot3a^{-4}b^{-3}), we have ((4\times3)a^{3+( - 4)}b^{2+( - 3)} = 12a^{-1}b^{-1}=\frac{12}{ab})
  10. For (x^{2}y^{-4}\cdot x^{3}y^{2}), we get (x^{2+3}y^{-4 + 2}=x^{5}y^{-2}=\frac{x^{5}}{y^{2}})

Step2: Use power - of - a - power rule ((a^{m})^{n}=a^{mn}) and (a^{0}=1) ((a\neq0))

  1. For ((x^{2})^{0}), by the power - of - a - power rule and (a^{0}=1), the result is (1)
  2. For ((2x^{2})^{-4}), we have (2^{-4}(x^{2})^{-4}=\frac{1}{2^{4}}x^{-8}=\frac{1}{16x^{8}})
  3. For ((4r^{0})^{4}), since (r^{0}=1), we get (4^{4}\times1^{4}=256)
  4. For ((4a^{3})^{2}), we have (4^{2}(a^{3})^{2}=16a^{6})
  5. For ((3k^{4})^{4}), we get (3^{4}(k^{4})^{4}=81k^{16})
  6. For ((4xy)^{-1}), we have (\frac{1}{4xy})

Answer:

  1. (4m^{5})
  2. (2m)
  3. (\frac{8}{r})
  4. (8n)
  5. (8k^{5})
  6. (4x^{2})
  7. (6xy^{2})
  8. (4v^{4}u^{2})
  9. (\frac{12}{ab})
  10. (\frac{x^{5}}{y^{2}})
  11. (1)
  12. (\frac{1}{16x^{8}})
  13. (256)
  14. (16a^{6})
  15. (81k^{16})
  16. (\frac{1}{4xy})