What is (sqrt(2^3mn^2))^4 ?

The solution to (sqrt(2^3mn^2))^4 is 64m^2n^4

Popular >

simplify (sqrt(2^3mn^2))^4

simplify

(2^{3} m n^{2})^{4}

64 m^{2} n^{4}

Solution steps

(2^{3} m n^{2})^{4}

Rewrite

4

2 \cdot 2

= (2^{3} m n^{2})^{2 \cdot 2}

Apply exponent rule:

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

assuming

a \geq 0

(2^{3} m n^{2})^{2 \cdot 2} = ((2^{3} m n^{2})^{2})^{2}

= ((2^{3} m n^{2})^{2})^{2}

Apply exponent rule:

assuming

n i s o dd or a \geq 0

(2^{3} m n^{2})^{2} = 2^{3} m n^{2}

= (2^{3} m n^{2})^{2}

Apply exponent rule:

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

(2^{3} m n^{2})^{2} = (2^{3})^{2} m^{2} (n^{2})^{2}

= (2^{3})^{2} m^{2} (n^{2})^{2}

(2^{3})^{2} = 64

= 64 m^{2} (n^{2})^{2}

Simplify

(n^{2})^{2} : n^{4}

= 64 m^{2} n^{4}

- e^{- l n (\frac{1}{2})}

(x^{2} + 2)^{- 4}

1 0^{10} (1.602 \cdot 1 0^{- 19}) (1340 + 461.3)

- 6 e^{- 0.05 (30)}

(- 1)^{n} (- 4)^{n}