Question

properties of exponents: true or false
determine if each equation is true or false. circle your answers.

1. $3^{4}cdot3^{3}=3^{7}$ true false
2. $(6^{4})^{2}=8^{8}$ true false
3. $\frac{4^{8}}{4^{4}} = 4^{4}$ true false
4. $\frac{9^{7}}{9^{7}}=9^{0}$ true false
5. $5^{3}cdot5^{2}=5^{6}$ true false
6. $1 = 2^{0}$ true false
7. $(2^{4})^{3}=2^{9}$ true false
8. $5^{-3}=\frac{1}{5^{3}}$ true false
9. $9^{6}cdot9^{-3}=9^{3}$ true false
10. $\frac{6^{17}}{6^{17}}=6^{0}$ true false
11. $(7^{4})^{2}cdot7^{10}=7^{18}$ true false
12. $\frac{1}{2^{8}cdot2^{6}}=2^{-14}$ true false
13. $\frac{(4^{2})^{3}}{4^{9}}=4^{2}$ true false
14. $\frac{12^{3}}{12^{5}}=\frac{1}{12^{2}}$ true false
15. $\frac{4^{8}cdot4^{10}}{4^{2}}=4^{40}$ true false

challenge!
correct all of the false equations. change one side of each false equation to make it true.

Explanation:

Step1: Recall exponent - product rule

$a^m\cdot a^n=a^{m + n}$. For $3^4\cdot3^3$, we have $3^4\cdot3^3=3^{4 + 3}=3^7$, so it's True.

Step2: Recall exponent - power rule

$(a^m)^n=a^{mn}$. For $(6^2)^3$, $(6^2)^3=6^{2\times3}=6^6$, so it's False.

Step3: Recall exponent - quotient rule

$\frac{a^m}{a^n}=a^{m - n}$. For $\frac{4^8}{4^2}$, $\frac{4^8}{4^2}=4^{8 - 2}=4^6$, so it's False.

Step4: Recall exponent - quotient rule

$\frac{9^7}{9^7}=9^{7 - 7}=9^0 = 1$, so it's False.

Step5: Recall exponent - product rule

$5^3\cdot5^2=5^{3+2}=5^5$, so it's False.

Step6: Recall zero - exponent rule

$a^0 = 1$ for $a
eq0$. So $1 = 2^0$ is True.

Step7: Recall exponent - power rule

$(2^4)^2=2^{4\times2}=2^8$, so it's False.

Step8: Recall negative - exponent rule

$a^{-n}=\frac{1}{a^n}$. So $5^{-3}=\frac{1}{5^3}$ is True.

Step9: Recall exponent - product rule

$9^6\cdot9^{-3}=9^{6+( - 3)}=9^3$, so it's False.

Step10: Recall exponent - quotient rule

$\frac{6^{17}}{6^{17}}=6^{17 - 17}=6^0$, so it's True.

Step11: Recall exponent - power and product rules

$(7^3)^2\cdot7^{10}=7^{3\times2}\cdot7^{10}=7^6\cdot7^{10}=7^{6 + 10}=7^{16}$, so it's True.

Step12: Recall exponent - product and negative - exponent rules

$\frac{1}{2^8\cdot2^6}=\frac{1}{2^{8 + 6}}=2^{-(8 + 6)}=2^{-14}$, so it's True.

Step13: Recall exponent - power and quotient rules

$\frac{(4^2)^3}{4^9}=\frac{4^{2\times3}}{4^9}=\frac{4^6}{4^9}=4^{6 - 9}=4^{-3}$, so it's False.

Step14: Recall exponent - quotient rule

$\frac{12^3}{12^3}=12^{3 - 3}=12^0 = 1$, and $\frac{1}{12^0}=1$, so it's True.

Step15: Recall exponent - product and quotient rules

$\frac{4^8\cdot4^{10}}{4^2}=4^{8 + 10-2}=4^{16}$, so it's False.

Answer:

1. True
2. False
3. False
4. False
5. False
6. True
7. False
8. True
9. False
10. True
11. True
12. True
13. False
14. True
15. False