Back to 1.2 Exponents and Scientific Notation

Simplifying Exponential Expressions

Avg difficulty 2.5

Simplify each expression and write the answer with positive exponents only.

  1. ⓐ ( 6 m 2 n −1 ) 3 \left(6 m^{2} n^{−1}\right)^{3}
  2. ⓑ 17 5 ⋅ 17 −4 ⋅ 17 −3 17^{5} \cdot 17^{−4} \cdot 17^{−3}
  3. ⓒ ( u −1 v v −1 ) 2 \left(\frac{u^{−1} v}{v^{−1}}\right)^{2}
  4. ⓓ ( −2 a 3 b −1 )( 5 a −2 b 2 ) \left(−2 a^{3} b^{−1}\right) \left(5 a^{−2} b^{2}\right)
  5. ⓔ ( x 2 2 ) 4 ( x 2 2 ) −4 \left(x^{2} \sqrt{2}\right)^{4} \left(x^{2} \sqrt{2}\right)^{−4}
  6. ⓕ ( 3 w 2 ) 5 ( 6 w −2 ) 2 \frac{\left(3 w^{2}\right)^{5}}{\left(6 w^{−2}\right)^{2}}

OpenStax Algebra and Trigonometry 2e, 1.2 Exponents and Scientific Notation, exercise 17

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Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.