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Popular >

simplify ((((-2)^2)^3)^4)^{1/3}

Solution

simplify

((((- 2)^{2})^{3})^{4})^{\frac{1}{3}}

Solution

256

Solution steps

((((- 2)^{2})^{3})^{4})^{\frac{1}{3}}

((- 2)^{2})^{3} : (- 2)^{6}

= (((- 2)^{6})^{4})^{\frac{1}{3}}

Apply exponent rule:

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

= ((- 2)^{6})^{4 \cdot \frac{1}{3}}

4 \cdot \frac{1}{3} = \frac{4}{3}

= ((- 2)^{6})^{\frac{4}{3}}

(- 2)^{6} = 2^{6}

= (2^{6})^{\frac{4}{3}}

Apply exponent rule:

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

= 2^{6 \cdot \frac{4}{3}}

6 \cdot \frac{4}{3} = 8

= 2^{8}

2^{8} = 256

= 256

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Frequently Asked Questions (FAQ)

What is ((((-2)^2)^3)^4)^{1/3} ?
The solution to ((((-2)^2)^3)^4)^{1/3} is 256