What is 7.8(20)^{-0.5} ?

The solution to 7.8(20)^{-0.5} is 1.74413…

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simplify 7.8(20)^{-0.5}

simplify

7.8 (20)^{- 0.5}

1.74413 \dots

Solution steps

7.8 (20)^{- 0.5}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 7.8 \cdot \frac{1}{20}

\frac{1}{20} = \frac{1}{2 5}

= 7.8 \cdot \frac{1}{2 5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 7.8}{2 5}

Multiply the numbers:

1 \cdot 7.8 = 7.8

= \frac{7.8}{2 5}

Convert element to a decimal form

5 = 2.23606 \dots

= \frac{7.8}{2 \cdot 2.23606 \dots}

Multiply the numbers:

2 \cdot 2.23606 \dots = 4.47213 \dots

= \frac{7.8}{4.47213 \dots}

Divide the numbers:

\frac{7.8}{4.47213 \dots} = 1.74413 \dots

= 1.74413 \dots

55.76 \cdot 1 0^{- 9} \cdot 1

\frac{- \frac{1}{2}}{- \frac{1}{8}}

(3 x 1 0^{4}) (2.3 x 1 0^{3})