Day 7 Hw. Need help on 1-8. Write answers in radical form

Answer:

Step-by-step explanation:

1) 3^1/4 • 3^1/4

We know that, a^m • a^n = a^(m + n) 

So, 

3^1/4 • 3^1/4 = 3^(1/4 + 1/4) 

= 3^(2/4)

= 3^(1/2) 

= √3

2) (2^1/6)^3

We know that, (a^m)^n = a^(m × n) 

So, 

(2^1/6)^3 = 2^(1/6 × 3) 

= 2^(3/6) 

= 2^(1/2) 

= √2

3) (5^3/8)/(5^1/8) 

We know that, (a^m)/(a^n) = a^(m - n) 

So, 

(5^3/8)/(5^1/8) = 5^(3/8 - 1/8) 

= 5^(2/8) 

= 5^(1/4)

= ⁴√5

4) 6^1/3 • 6^1/2

We know that, a^m • a^n = a^(m + n) 

So, 

6^1/3 • 6^1/2 = 6^(1/3 + 1/2) 

= 6^(5/6)

= 6√(6^5) 

5) (4^2/3)^1/2

We know that, (a^m)^n = a^(m × n) 

So, 

(4^2/3)^1/2 = 4^(2/3 × 1/2) 

= 4^(2/6) 

= 4^(1/3) 

= ³√4

6) 9^3/9^(5/2)

 We know that, (a^m)/(a^n) = a^(m - n) 

So, 

9^3/9^(5/2) = 9^(3 - 5/2) 

= 9^(1/2) 

= √9

= 3

7) (25a^4 b^6)^1/2

= (5^2)^1/2 • (a^4)^1/2 • (b^6)^1/2

= 5 • a^2 • b^3

= 5a^2 b^3

8) (8x^6 y^12)^1/3

= (2^3)^1/3 • (x^6)^1/3 • (y^12)^1/3

= 2 • x^2 • y^4

= 2x^2 y^4