Exponents and scientific notation

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. 62⋅65=6?6^{ 2 } \cdot 6^{ 5 } = 6^{?}. What is the exponent?
  2. 312÷35=3?3^{ 12 } \div 3^{ 5 } = 3^{?}. What is the exponent?
  3. (94)4=9?\left(9^{ 4 }\right)^{ 4 } = 9^{?}. What is the exponent?
  4. Write 5−15^{-1} as a fraction.
  5. 106⋅10−9=10?10^{ 6 } \cdot 10^{-9} = 10^{?}. What is the exponent?
  6. What is 51051^0?
  7. Write 900000000900000000 in scientific notation as 9×10?9 \times 10^{?}. What is the exponent?
  8. How many times as large as 8×1048 \times 10^{ 4 } is 8×1078 \times 10^{ 7 }?
  9. When 2×10−62 \times 10^{-6} is written as a decimal, how many zeros are there between the decimal point and the digit 2?
  10. Compute (3×104)⋅(2×102)(3 \times 10^{ 4 }) \cdot (2 \times 10^{ 2 }). (An expression with a power of 10 is fine.)
  11. Compute (4×109)÷(2×104)(4 \times 10^{ 9 }) \div (2 \times 10^{ 4 }). (An expression with a power of 10 is fine.)
  12. Compute 2×104+2×1042 \times 10^{ 4 } + 2 \times 10^{ 4 }. (An expression with a power of 10 is fine.)