MIA · Mixed set · Unit 5

1. 1.

   Simplify 3^2 · 3^4. Write as a power.

   Answer. 3^6

   Add exponents: 3^{2+4} = 3^6.

2. 2.

   Evaluate 10^0.

   Answer. 1

   Any nonzero number to the power 0 is 1.

3. 3.

   Write 4 × 10^2 as an ordinary number.

   Answer. 400

   Move the decimal 2 places right: 400.

4. 4.

   Compute (6.8 × 10^3) × (2 × 10^2). Write in scientific notation.

   Answer. 1.36 × 10^6

   Multiply coefficients and add exponents, then adjust so the coefficient is at least 1 and less than 10.

5. 5.

   Simplify 3^93^4. Write as a power. Then Luis needs 3 of that amount. What is the total they need?

   Answer. 9^5

   Subtract exponents: 3^{9-4} = 3^5. Then multiply by 3: 9^5.

6. 6.

   Evaluate 10^0. Then Sam needs 5 of that amount. What is the total they need?

   Answer. 5

   Any nonzero number to the power 0 is 1. Then multiply by 5: 5.

7. 7.

   Write 20000 as a product of a digit and a power of 10. Then Elena needs 5 of that amount. What is the total they need?

   Answer. 10 × 10^4

   20000 = 2 × 10^4. Then multiply by 5: 10 × 10^4.

8. 8.

   Compute (7.9 × 10^5) × (2 × 10^2). Write in scientific notation. Then Priya needs 4 of that amount. What is the total they need?

   Answer. 6.32 × 10^8

   Multiply coefficients and add exponents, then adjust so the coefficient is at least 1 and less than 10. Then multiply by 4: 6.32 × 10^8.

9. 9.

   Simplify (5^2)^3. Write as a power. Then Owen needs 2 of that amount. What is the total they need?

   Answer. 10^6

   Multiply exponents: 5^{2·3} = 5^6. Then multiply by 2: 10^6.

10. 10.

    Evaluate 10^0. Then Sam needs 5 of that amount. What is the total they need?

    Answer. 5

    Any nonzero number to the power 0 is 1. Then multiply by 5: 5.

11. 11.

    Think

    Luis tried this problem:
    Write 4 × 10^2 as an ordinary number.
    Luis wrote 800. That is not correct. What is the right answer?

    Answer. 400

    Luis’s answer 800 is off. Move the decimal 2 places right: 400.

12. 12.

    Think

    Grace tried this problem:
    Compute (8.4 × 10^6) × (2 × 10^2). Write in scientific notation.
    Grace wrote 0.68 × 10^9. That is not correct. What is the right answer?

    Answer. 1.68 × 10^9

    Grace’s answer 0.68 × 10^9 is off. Multiply coefficients and add exponents, then adjust so the coefficient is at least 1 and less than 10.

Original extra practice. Keys are computed from the items, not guessed.