What is 5sqrt(5)*(5^3)/(5^{-3/2)} ?

The solution to 5sqrt(5)*(5^3)/(5^{-3/2)} is 15625

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simplify 5sqrt(5)*(5^3)/(5^{-3/2)}

simplify

55 \cdot \frac{5 ^{3}}{5 ^{- \frac{3}{2}}}

15625

Solution steps

55 \frac{5 ^{3}}{5 ^{- \frac{3}{2}}}

Cancel

\frac{5 ^{3}}{5 ^{- \frac{3}{2}}} : 625 \cdot 5^{\frac{1}{2}}

= 55 \cdot 625 \cdot 5^{\frac{1}{2}}

Multiply the numbers:

5 \cdot 625 = 3125

= 31255 \cdot 5^{\frac{1}{2}}

= 5^{\frac{1}{2}} \cdot 31255

Apply radical rule:

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

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

= 5^{\frac{1}{2}} \cdot 3125 \cdot 5^{\frac{1}{2}}

Apply exponent rule:

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

5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} = 5^{\frac{1}{2} + \frac{1}{2}}

= 5^{\frac{1}{2} + \frac{1}{2}} \cdot 3125

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

= 5^{1} \cdot 3125

Apply exponent rule:

a^{1} = a

5^{1} = 5

= 5 \cdot 3125

Multiply the numbers:

5 \cdot 3125 = 15625

= 15625

(- \frac{7}{9})^{- 2} l e f t (- \frac{7}{9})^{- 5}

1.35 (2.802) e^{- 2.802 (2.802)}

\frac{( x + 2 ) ^{2}}{( x + 1 ) ^{2}}

(1 + x) (1 - 2 x)^{- \frac{1}{2}}

20 \cdot \frac{1}{8} \cdot e^{- 0.0675 \cdot 5}

What is 5sqrt(5)*(5^3)/(5^{-3/2)} ?
The solution to 5sqrt(5)*(5^3)/(5^{-3/2)} is 15625