Exponent Practice Problems – Test 1

  1. \(10^4\) is NOT equal to which of the following?
  1. \(100,000\)
  2. \(0.1 \times 10^5\)
  3. \(10 \times 10 \times 10 \times 10\)
  4. \(10^2 \times 10^2\)
  5. \(10,000\)
Show Answer
The correct answer is A!

\(10^4\) is not equal to 100,000. To equal 100,000, you would need \(10^5\).

 

  1. Multiply 104 by 102.
  1. 108
  2. 102
  3. 106
  4. 10-2
  5. 103
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The correct answer is C!

When multiplying terms with the same base, the exponents should be added. Thus, \(10^4 \times 10^2=10^6\).

 

  1. Divide \(x^5\) by \(x^2\).
  1. \(x^7\)
  2. \(x^4\)
  3. \(x^{10}\)
  4. \(x^3\)
  5. \(x^{2.5}\)
Show Answer
The correct answer is D!

When dividing terms with the same base, the exponents should be subtracted. Thus, \(\tfrac{x^5}{x^2}\) \(=x^3\).

 

  1. Multiply 8.23 by 109.
  1. 0.00000000823
  2. 0.000000823
  3. 8.23
  4. 8230000000
  5. 823000000000
Show Answer
The correct answer is D!

The decimal will be moved to the right nine places. Thus, seven zeros will be added to the right of 823, giving 8,230,000,000.

 

  1. Which of the following is equal to 83,000?
  1. \(83 \times 10^4\)
  2. \(8.3 \times 10^4\)
  3. \(8.3 \times 10^3\)
  4. \(83 \times 10^5\)
  5. \(83 \times 10\)
Show Answer
The correct answer is B!

Moving the decimal to the right of the digit 8 gives the equivalent expression \(8.3\times 10^4\), since there are four digits to the right of the 8.

 

  1. Which of the following is equal to 0.00875?
  1. \(8.75 \times 10^{-2}\)
  2. \(8.75 \times 10^{-3}\)
  3. \(8.75 \times 10^{-4}\)
  4. \(87.5 \times 10^{-3}\)
  5. \(875 \times 10^{-4}\)
Show Answer
The correct answer is B!

Moving the decimal to the right of the 8 gives \(8.75\times 10^{-3}\), since the decimal must be moved three places to the right.