What is 32^{1/8}*32^{3/8} ?

The solution to 32^{1/8}*32^{3/8} is 4*2^{1/2}

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simplify 32^{1/8}*32^{3/8}

simplify

3 2^{\frac{1}{8}} \cdot 3 2^{\frac{3}{8}}

4 \cdot 2^{\frac{1}{2}}

Solution steps

3 2^{\frac{1}{8}} \cdot 3 2^{\frac{3}{8}}

Apply exponent rule:

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

3 2^{\frac{1}{8}} \cdot 3 2^{\frac{3}{8}} = 3 2^{\frac{1}{8} + \frac{3}{8}}

= 3 2^{\frac{1}{8} + \frac{3}{8}}

\frac{1}{8} + \frac{3}{8} = \frac{1}{2}

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

Prime factorization of

32 : 2^{5}

= (2^{5})^{\frac{1}{2}}

Apply exponent rule:

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

2^{5} = 2^{4} \cdot 2

= (2^{4} \cdot 2)^{\frac{1}{2}}

Apply exponent rule:

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

(2^{4} \cdot 2)^{\frac{1}{2}} = (2^{4})^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}

= (2^{4})^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}

(2^{4})^{\frac{1}{2}} = 4

= 4 \cdot 2^{\frac{1}{2}}

3 x^{2} + 11 x - 20 = 0

5 ∣ x - 1 ∣ - 4 > 31

12 + \frac{x}{5} = 12

- 8 (2 x + 8) \geq - 4 (4 x + 2)

49 x^{2} + 36 = 0