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Popular >

simplify (10^3)^{1/2}

Solution

simplify

(1 0^{3})^{\frac{1}{2}}

Solution

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

+1

Decimal Notation

31.62277 \dots

Solution steps

(1 0^{3})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 1 0^{3 \cdot \frac{1}{2}}

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

= 1 0^{\frac{3}{2}}

1 0^{\frac{3}{2}} = 1 0^{1 + \frac{1}{2}}

= 1 0^{1 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

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

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Frequently Asked Questions (FAQ)

What is (10^3)^{1/2} ?
The solution to (10^3)^{1/2} is 10*10^{1/2}