UA · Unit 5 review

1. 1.

   Simplify 5^5 · 5^4. Write as a power.

   Answer. 5^9

   Add exponents: 5^{5+4} = 5^9.

2. 2.

   Evaluate 10^0.

   Answer. 1

   Any nonzero number to the power 0 is 1.

3. 3.

   Write 700 as a product of a digit and a power of 10.

   Answer. 7 × 10^2

   700 = 7 × 10^2.

4. 4.

   Compute (8.7 × 10^4) × (2 × 10^2). Write in scientific notation.

   Answer. 1.74 × 10^7

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

5. 5.

   Simplify 2^72^3. Write as a power. Then Owen needs 4 of that amount. What is the total they need?

   Answer. 8^4

   Subtract exponents: 2^{7-3} = 2^4. Then multiply by 4: 8^4.

6. 6.

   Evaluate 10^0. Then Ava 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 50000 as a product of a digit and a power of 10. Then Sam needs 4 of that amount. What is the total they need?

   Answer. 20 × 10^4

   50000 = 5 × 10^4. Then multiply by 4: 20 × 10^4.

8. 8.

   Compute (6.3 × 10^3) × (2 × 10^2). Write in scientific notation. Then Luis needs 4 of that amount. What is the total they need?

   Answer. 5.04 × 10^6

   Multiply coefficients and add exponents, then adjust so the coefficient is at least 1 and less than 10. Then multiply by 4: 5.04 × 10^6.

9. 9.

   Simplify (4^5)^2. Write as a power. Then Sam needs 3 of that amount. What is the total they need?

   Answer. 12^10

   Multiply exponents: 4^{5·2} = 4^10. Then multiply by 3: 12^10.

10. 10.

    Evaluate 10^0. Then Ava needs 3 of that amount. What is the total they need?

    Answer. 3

    Any nonzero number to the power 0 is 1. Then multiply by 3: 3.

11. 11.

    Think

    Mei tried this problem:
    Write 800000 as a product of a digit and a power of 10.
    Mei wrote -8 × 10^5. That is not correct. What is the right answer?

    Answer. 8 × 10^5

    Mei’s answer -8 × 10^5 is off. 800000 = 8 × 10^5.

12. 12.

    Think

    Sam tried this problem:
    Compute (3.3 × 10^3) × (2 × 10^2). Write in scientific notation.
    Sam wrote 13.2 × 10^5. That is not correct. What is the right answer?

    Answer. 6.6 × 10^5

    Sam’s answer 13.2 × 10^5 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.