Match each whole number with a rational, exponential expression. 1. 256 2. 9 3. 16 4. 25 5. 225 6. 196
Question:
1. 256
2. 9
3. 16
4. 25
5. 225
6. 196
Answers
256 = 16^2
9 = 3^2
16 = 4^2
25 = 5^2
225 = 15^2
196 = 14^2
1) 92) 163) 2254) 145) 256) 256(by the way, it should be "cube root" instead of "3 square root". also, question 6 is 4096, not 4069.)
1)16^2 or 4^4
2)3^2
3)4^2
4)5^2
5)15^2
6)14^2
1. 343^(2/3)
3rdrt[(343(343)]
49
2. [2,197^(1/3)]^2
[3rdrt(2,197)]^2
169
3. 729^(2/3)
3rdrt[729(729)]
81
4. (1,000^2)^(1/3)
3rdrt(1,000^2)
100
5. [3rdrt(9261)]^2
441
6. [3rdrt(216^2)]
36
Hope this helps!
1. 9
2. 16
3. 225
4. 196
5. 25
6. 256
1. 343^2/3 = 49
2. (2197^1/3)² = 169
3. 729^2/3 = 81
4. (1000²)^1/3 = 100
5. (³√9261)² = 441
6. ³√216² = 36
Hope this helps.
1)
[tex]\displaystyle\left(8^{4}\right)^{\frac{3}{4}}=8^3=512[/tex]
2)
[tex]\displaystyle\left(\sqrt[4]{81}\right)^{3}=3^3=27[/tex]
3)
[tex]\displaystyle 1296^{\frac{3}{4}}=6^3=216[/tex]
4)
[tex]\displaystyle 16^{\frac{3}{4}}=2^3=8[/tex]
5)
[tex]\displaystyle\left(\sqrt[4]{2401}\right)^{3}=7^3=343[/tex]
6)
[tex]\displaystyle \left(6561^{\frac{1}{4}}\right)^{3}=9^3=729[/tex]
1. 2^9 = 512
2. 2^3 = 8
3. 7^3 = 343
4. 6^3 = 216
5. 3^6 = 729
Step-by-step explanation:
To start we have to express the number as a multiplication of prime numbers, from there we can take the expression as a power
1.
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
2^9 = 512
2.
2 x 2 x 2 = 8
2^3 = 8
3.
7 x 7 x 7 = 343
7^3 = 343
4.
6 x 6 x 6 = 216
6^3 = 216
5.
3 x 3 x 3 x 3 x 3 x 3 = 729
3^6 = 729
1. 49
2. 169
3. 81
4. 100
5. 441
6. 36
Step-by-step explanation:
1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]
= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]
= 7×7 = 49
2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]
= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]
= 169
3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]
= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]
= 81
4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]
= 10²
= 100
5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]
= 21²
= 441
6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]
= 6²
= 36
216 - 6^3
512 - 2^9
8 - 2^3
729 - 3^6
27 - 3^3
343 - 7^3