# 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