simplify 5sqrt(-27)

Solution

simplify

5 - 27

153 i

Solution steps

5 - 27

Prime factorization of

27 : 3^{3}

= 5 - 3^{3}

Apply exponent rule:

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

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

= 5 - 3^{2} \cdot 3

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

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

= 5 3^{2} - 3

Apply radical rule:

a^{2} = a, a \geq 0

3^{2} = 3

= 5 \cdot 3 - 3

Multiply the numbers:

5 \cdot 3 = 15

= 15 - 3

Apply radical rule:

- a = a - 1

- 3 = 3 - 1

= 153 - 1

Apply imaginary number rule:

- 1 = i

= 153 i

lo g_{3} (\frac{1}{3 ^{3}})

\frac{( 1 + 2 ^{(- 3 s)} + 9 ^{2} - 2 s ^{3} )}{( s ^{2} ( s - 2 ) ^{2} )}

6 x^{2} - 2 x y + 3 x^{2}

\frac{7 m n ^{4} p ^{5}}{21 m ^{3} n p ^{7}}

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