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Popular >

simplify 50^{3/2}

Solution

simplify

5 0^{\frac{3}{2}}

Solution

250 \cdot 2^{\frac{1}{2}}

+1

Solution steps

5 0^{\frac{3}{2}}

Prime factorization of

50 : 2 \cdot 5^{2}

= (2 \cdot 5^{2})^{\frac{3}{2}}

Apply exponent rule:

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

(2 \cdot 5^{2})^{\frac{3}{2}} = 2^{\frac{3}{2}} (5^{2})^{\frac{3}{2}}

= 2^{\frac{3}{2}} (5^{2})^{\frac{3}{2}}

(5^{2})^{\frac{3}{2}} = 125

= 2^{\frac{3}{2}} \cdot 125

2^{\frac{3}{2}} = 2 \cdot 2^{\frac{1}{2}}

= 2 \cdot 125 \cdot 2^{\frac{1}{2}}

Multiply the numbers:

2 \cdot 125 = 250

= 250 \cdot 2^{\frac{1}{2}}

Popular Examples

simplify sqrt(x^3)simplify

x^{3}

6 x + 8 = 9 x - 4

simplify (x^{-3})/(x^{-9)}simplify

\frac{x ^{- 3}}{x ^{- 9}}

6 x^{2} + 40 x + 50 = 0

factor 7x^4+51x^2+14 factor

7 x^{4} + 51 x^{2} + 14

Frequently Asked Questions (FAQ)

What is 50^{3/2} ?
The solution to 50^{3/2} is 250*2^{1/2}