What is sqrt(10^{4-log_{10)(25)}} ?

The solution to sqrt(10^{4-log_{10)(25)}} is 10^{(-2log_{10}(5)+4)/2}

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simplify sqrt(10^{4-log_{10)(25)}}

simplify

1 0^{4 - l o g_{10} (25)}

1 0^{\frac{- 2 l o g _{10} ( 5 ) + 4}{2}}

Decimal Notation

20

Solution steps

1 0^{4 - l o g_{10} (25)}

Apply radical rule:

a = a^{\frac{1}{2}}

= (1 0^{4 - l o g_{10} (25)})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 1 0^{(4 - l o g_{10} (25)) \frac{1}{2}}

(4 - lo g_{10} (25)) \frac{1}{2} = \frac{4 - 2 lo g _{10} ( 5 )}{2}

= 1 0^{\frac{4 - 2 l o g _{10} ( 5 )}{2}}

= 1 0^{\frac{- 2 l o g _{10} ( 5 ) + 4}{2}}

7.41 \cdot 1 0^{- 3}

2 \cdot e^{-, 333}

0.5 e^{2 t} \cdot e^{- 2 t}

(14 \cdot 1 0^{- 3}) \cdot 9.8

(3 m g^{2}) \cdot (0.012 g)

What is sqrt(10^{4-log_{10)(25)}} ?
The solution to sqrt(10^{4-log_{10)(25)}} is 10^{(-2log_{10}(5)+4)/2}