What is (9^{1/2}*27^{1/3})^{1/2} ?

The solution to (9^{1/2}*27^{1/3})^{1/2} is 3

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simplify (9^{1/2}*27^{1/3})^{1/2}

simplify

(9^{\frac{1}{2}} \cdot 2 7^{\frac{1}{3}})^{\frac{1}{2}}

3

Solution steps

(9^{\frac{1}{2}} \cdot 2 7^{\frac{1}{3}})^{\frac{1}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(9^{\frac{1}{2}} \cdot 2 7^{\frac{1}{3}})^{\frac{1}{2}} = (9^{\frac{1}{2}})^{\frac{1}{2}} (2 7^{\frac{1}{3}})^{\frac{1}{2}}

= (9^{\frac{1}{2}})^{\frac{1}{2}} (2 7^{\frac{1}{3}})^{\frac{1}{2}}

(9^{\frac{1}{2}})^{\frac{1}{2}} = 3^{\frac{1}{2}}

= 3^{\frac{1}{2}} (2 7^{\frac{1}{3}})^{\frac{1}{2}}

(2 7^{\frac{1}{3}})^{\frac{1}{2}} = 3^{\frac{1}{2}}

= 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} = 3^{\frac{1}{2} + \frac{1}{2}}

= 3^{\frac{1}{2} + \frac{1}{2}}

Add similar elements:

\frac{1}{2} + \frac{1}{2} = 2 \cdot \frac{1}{2}

= 3^{2 \cdot \frac{1}{2}}

Multiply

2 \cdot \frac{1}{2} : 1

= 3^{1}

Apply rule

a^{1} = a

= 3

∣ t + 2 ∣ \leq 4

(- 7.4) + l = 9.11

w^{2} + w - 42

9 - 12

- 11 f = 7 (1 - 2 f) + 5

What is (9^{1/2}*27^{1/3})^{1/2} ?
The solution to (9^{1/2}*27^{1/3})^{1/2} is 3