Mathematics
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09.01.2020

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

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16.02.2023, solved by verified expert

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**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**

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