L19 · Exponent properties for positive integers

1. 1.

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

   Answer. 4^7

   Add exponents: 4^{3+4} = 4^7.

2. 2.

   Simplify 5^85^4. Write as a power.

   Answer. 5^4

   Subtract exponents: 5^{8-4} = 5^4.

3. 3.

   Simplify (2^5)^2. Write as a power.

   Answer. 2^10

   Multiply exponents: 2^{5·2} = 2^10.

4. 4.

   Simplify 2^5 · 2^4. Write as a power.

   Answer. 2^9

   Add exponents: 2^{5+4} = 2^9.

5. 5.

   Simplify 3^73^2. Write as a power. Then Jonah needs 2 of that amount. What is the total they need?

   Answer. 6^5

   Subtract exponents: 3^{7-2} = 3^5. Then multiply by 2: 6^5.

6. 6.

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

   Answer. 10^16

   Multiply exponents: 5^{4·4} = 5^16. Then multiply by 2: 10^16.

7. 7.

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

   Answer. 6^8

   Add exponents: 3^{4+4} = 3^8. Then multiply by 2: 6^8.

8. 8.

   Simplify 4^84^4. Write as a power. Then Theo needs 4 of that amount. What is the total they need?

   Answer. 16^4

   Subtract exponents: 4^{8-4} = 4^4. Then multiply by 4: 16^4.

9. 9.

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

   Answer. 8^4

   Multiply exponents: 4^{2·2} = 4^4. Then multiply by 2: 8^4.

10. 10.

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

    Answer. 8^8

    Add exponents: 2^{4+4} = 2^8. Then multiply by 4: 8^8.

11. 11.

    Think

    Malik tried this problem:
    Simplify 3^73^2. Write as a power.
    Malik wrote 2^5. That is not correct. What is the right answer?

    Answer. 3^5

    Malik’s answer 2^5 is off. Subtract exponents: 3^{7-2} = 3^5.

12. 12.

    Think

    Malik tried this problem:
    Simplify (5^4)^3. Write as a power.
    Malik wrote 6^12. That is not correct. What is the right answer?

    Answer. 5^12

    Malik’s answer 6^12 is off. Multiply exponents: 5^{4·3} = 5^12.

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