38 Practice: Exponents and Scientific Notation (6.1 – 6.3) — Intermediate Algebra

6.1 Working With Exponents

Simplify the following.

  1. 4\cdot 4^4\cdot 4^4
  2. 4\cdot 4^4\cdot 4^2
  3. 2m^4n^2\cdot 4nm^2
  4. x^2y^4\cdot xy^2
  5. (3^3)^4
  6. (4^3)^4
  7. (2u^3v^2)^2
  8. (xy)^3
  9. 4^5 \div 4^3
  10. 3^7 \div 3^3
  11. 3nm^2 \div 3n
  12. x^2y^4 \div 4xy
  13. (x^3y^4\cdot 2x^2y^3)^2
  14. [(u^2v^2)(2u^4)]^3
  15. [(2x)^3 \div x^3]^2
  16. (2a^2b^2a^7) \div (ba^4)^2
  17. [(2y^{17}) \div (2x^2y^4)^4]^3
  18. [(xy^2)(y^4)^2] \div 2y^4
  19. (2xy^5\cdot 2x^2y^3) \div (2xy^4\cdot y^3)
  20. (2y^3x^2) \div [(x^2y^4)(x^2)]
  21. [(q^3r^2)(2p^2q^2r^3)^2] \div 2p^3
  22. (2x^4y^5)(2z^{10}x^2y^7) \div (xy^2z^2)^4

6.2 Negative Exponents

Simplify. Your answer should contain only positive exponents.

  1. (2x^4y^{-2})(2xy^3)^4
  2. (2a^{-2}b^{-3})(2a^0b^4)^4
  3. (2x^2y^2)^4x^{-4}
  4. [(m^0n^3)(2m^{-3}n^{-3})]^0
  5. (2x^{-3}y^2)\div (3x^{-3}y^3\cdot 3x^0)
  6. 3y^3\div [(3yx^3)(2x^4y^{-3})]
  7. 2y\div (x^0y^2)^4
  8. (a^4)^4\div 2b
  9. (2a^2b^3)^4\div a^{-1}
  10. (2y^{-4})^{-2}\div x^2
  11. (2mn)^4\div m^0n^{-2}
  12. 2x^{-3}\div (x^4y^{-3})^{-1}
  13. [(2u^{-2}v^3)(2uv^4)^{-1}]\div 2u^{-4}v^0
  14. [(2yx^2)(x^{-2})]\div (2x^0y^4)^{-1}
  15. b^{-1}\div [(2a^4b^0)^0(2a^{-3}b^2)]
  16. 2yzx^2\div [(2x^4y^4z^{-2})(zy^2)^4]
  17. [(cb^3)^2(2a^{-3}b^2)]\div (a^3b^{-2}c^3)^3
  18. 2q^4(m^2p^2q)\div (2m\cdot 4p^2)^3
  19. (yx^{-4}z^2)^{-1}\div z^3\cdot x^2y^3z^{-1}
  20. 2mpn^{-3}\div [2n^2p^0(m^0n^{-4}p^2)^3]

6.3 Scientific Notation

For questions 1 to 6, write each number in scientific notation.

  1. 885.3
  2. 0.000744
  3. 0.081
  4. 1.09
  5. 0.039
  6. 15,000

For questions 7 to 12, write each number in standard notation.

  1. 8.7 × 105
  2. 2.56 × 102
  3. 9 × 10−4
  4. 5 × 104
  5. 2 × 100
  6. 6 × 10−5

For questions 13 to 20, simplify each expression and write each answer in scientific notation.

  1. (7 × 10−1)(2 × 10−3)
  2. (2 × 10−6)(8.8 × 10−5)
  3. (5.26 × 10−5)(3.16 × 10−2)
  4. (5.1 × 106)(9.84 × 10−1)
  5. \dfrac{(2.6 \times 10^{-2})(6 \times 10^{-2})}{(4.9 \times 10^1)(2.7 \times 10^{-3})}
  6. \dfrac{(7.4 \times 10^4)(1.7 \times 10^{-4})}{(7.2 \times 10^{-1})(7.32 \times 10^{-1})}
  7. \dfrac{(5.33 \times 10^{-6})(9.62 \times 10^{-2})}{(5.5 \times 10^{-5})^2}
  8. \dfrac{(3.2 \times 10^{-3})(5.02 \times 10^0)}{(9.6 \times 10^3)^{-4}}

 

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