What is sqrt(\sqrt{\sqrt{(-4)^2*(-2)^5*(-1/2))}} ?

The solution to sqrt(\sqrt{\sqrt{(-4)^2*(-2)^5*(-1/2))}} is 2

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simplify sqrt(\sqrt{\sqrt{(-4)^2(-2)^5(-1/2))}}

simplify

(- 4)^{2} \cdot (- 2)^{5} \cdot (- \frac{1}{2})

2

Solution steps

(- 4)^{2} (- 2)^{5} (- \frac{1}{2})

Remove parentheses:

(- a) = - a

Apply radical rule:

= ((- (- 4)^{2} (- 2)^{5} \frac{1}{2})^{\frac{1}{4}})^{\frac{1}{2}}

Apply exponent rule:

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

= (- (- 4)^{2} (- 2)^{5} \frac{1}{2})^{\frac{1}{4} \cdot \frac{1}{2}}

\frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8}

= (- (- 4)^{2} (- 2)^{5} \frac{1}{2})^{\frac{1}{8}}

(- 4)^{2} = 4^{2}

(- 2)^{5} = - 2^{5}

Apply rule

- (- a) = a

Simplify

4^{2} \cdot 2^{5} \cdot \frac{1}{2} : 2^{9} \cdot \frac{1}{2}

Multiply

2^{9} \cdot \frac{1}{2} : 256

Factor the number:

256 = 2^{8}

Apply radical rule:

= 2

(\frac{( 12 )}{( 23 ) ^{2}})^{2}^{2}^{2}

1.73 \cdot 1 0^{- 5}

10000 \cdot e^{- \frac{3}{4} (2 - 3)^{\frac{4}{3}}}

2.35 \cdot 1 0^{- 3}

5^{- l o g_{5} (2)}

What is sqrt(\sqrt{\sqrt{(-4)^2*(-2)^5*(-1/2))}} ?
The solution to sqrt(\sqrt{\sqrt{(-4)^2*(-2)^5*(-1/2))}} is 2