What is (2^{sqrt(3)}*4)^{sqrt(3)-2} ?

The solution to (2^{sqrt(3)}*4)^{sqrt(3)-2} is 1/2

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simplify (2^{sqrt(3)}*4)^{sqrt(3)-2}

simplify

(2^{3} \cdot 4)^{3 - 2}

\frac{1}{2}

Decimal Notation

0.5

Solution steps

(2^{3} \cdot 4)^{3 - 2}

Apply exponent rule:

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

(2^{3} \cdot 4)^{3 - 2} = (2^{3})^{3 - 2} \cdot 4^{3 - 2}

= (2^{3})^{3 - 2} \cdot 4^{3 - 2}

(2^{3})^{3 - 2} = 2^{3 - 23}

= 2^{3 - 23} \cdot 4^{3 - 2}

Factor integer

4 = 2^{2}

= 2^{3 - 23} (2^{2})^{3 - 2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(2^{2})^{3 - 2} = 2^{2 (3 - 2)}

= 2^{3 - 23} \cdot 2^{2 (3 - 2)}

Apply exponent rule:

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

2^{3 - 23} \cdot 2^{2 (3 - 2)} = 2^{3 - 23 + 2 (3 - 2)}

= 2^{3 - 23 + 2 (3 - 2)}

Expand

3 - 23 + 2 (3 - 2) : - 1

= 2^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{2}

\frac{sin ( θ )}{cos ( θ )} + \frac{cos ( θ )}{sin ( θ )}

8 \times 5

(a + b + c + d)^{2}

x - \frac{x}{2}

\frac{12}{40}

What is (2^{sqrt(3)}*4)^{sqrt(3)-2} ?
The solution to (2^{sqrt(3)}*4)^{sqrt(3)-2} is 1/2