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Popular >

simplify 5sqrt(3)^{-2.5}

Solution

simplify

5 3^{- 2.5}

Solution

1.26639 \dots

Solution steps

5 (3)^{- 2.5}

(3)^{- 2.5} : 3^{- 1.25}

= 5 \cdot 3^{- 1.25}

Apply exponent rule:

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

3^{- 1.25} = \frac{1}{3 ^{1.25}}

= 5 \cdot \frac{1}{3 ^{1.25}}

Multiply fractions:

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

= \frac{1 \cdot 5}{3 ^{1.25}}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{3 ^{1.25}}

3^{1.25} = 3.94822 \dots

= \frac{5}{3.94822 \dots}

Divide the numbers:

\frac{5}{3.94822 \dots} = 1.26639 \dots

= 1.26639 \dots

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Frequently Asked Questions (FAQ)

What is 5sqrt(3)^{-2.5} ?
The solution to 5sqrt(3)^{-2.5} is 1.26639…