What is (sqrt(36-4))^30.5 ?

The solution to (sqrt(36-4))^30.5 is 64sqrt(2)

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simplify (sqrt(36-4))^30.5

simplify

(36 - 4)^{3} 0.5

642

Decimal Notation

90.50966 \dots

Solution steps

(36 - 4)^{3} \cdot 0.5

Apply exponent rule:

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

(36 - 4)^{2 + 1} = (36 - 4)^{2} 36 - 4

= (36 - 4)^{2} 36 - 4 \cdot 0.5

Apply exponent rule:

(36 - 4)^{2} = 36 - 4

= (36 - 4) 36 - 4 \cdot 0.5

Subtract the numbers:

36 - 4 = 32

= 3232 \cdot 0.5

Prime factorization of

32 : 2^{5}

= 32 2^{5} \cdot 0.5

Apply exponent rule:

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

2^{5} = 2^{4} \cdot 2

= 32 2^{4} \cdot 2 \cdot 0.5

Apply radical rule:

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

2^{4} \cdot 2 = 2^{4} 2

= 32 2^{4} 2 \cdot 0.5

2^{4} = 4

= 32 \cdot 42 \cdot 0.5

Multiply the numbers:

32 \cdot 4 = 128

= 1282 \cdot 0.5

Multiply the numbers:

128 \cdot 0.5 = 64

= 642

183 y^{5} x^{2} y

\frac{1}{2} e^{2 x} (e^{x})

x^{2} y \cdot x^{2} y \cdot Δ y_{2}

5.76 \cdot 1 0^{- 3}