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Popular >

simplify 1000^{3/2}

Solution

simplify

100 0^{\frac{3}{2}}

Solution

10000 \cdot 1 0^{\frac{1}{2}}

+1

Decimal Notation

31622.77660 \dots

Solution steps

100 0^{\frac{3}{2}}

Prime factorization of

1000 : 2^{3} \cdot 5^{3}

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

Apply exponent rule:

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

2^{3} \cdot 5^{3} = 2^{2} \cdot 2 \cdot 5^{2} \cdot 5

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

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

Apply exponent rule:

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

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

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

(2^{2})^{\frac{3}{2}} = 8

= 8 (5^{2})^{\frac{3}{2}} (2 \cdot 5)^{\frac{3}{2}}

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

= 8 \cdot 125 (2 \cdot 5)^{\frac{3}{2}}

(2 \cdot 5)^{\frac{3}{2}} = 10 \cdot 1 0^{\frac{1}{2}}

= 8 \cdot 125 \cdot 10 \cdot 1 0^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 125 \cdot 10 = 10000

= 10000 \cdot 1 0^{\frac{1}{2}}

Popular Examples

factor-5x^3-55x^2-150x factor

- 5 x^{3} - 55 x^{2} - 150 x

factor 3ax-2by-2bx-6a+3ay+4b factor

3 a x - 2 b y - 2 b x - 6 a + 3 a y + 4 b

simplify-(3/2+5/2 i)+(5/3+11/3 i)simplify

- (\frac{3}{2} + \frac{5}{2} i) + (\frac{5}{3} + \frac{11}{3} i)

(-3x-3)/5 =3-4(x+2)

\frac{- 3 x - 3}{5} = 3 - 4 (x + 2)

0.2 x^{2} + 1.2 = 3.4

Frequently Asked Questions (FAQ)

What is 1000^{3/2} ?
The solution to 1000^{3/2} is 10000*10^{1/2}