Simplify ((25x)^(3/2))/(5*x^(1/2))

$\frac{{(25 x)}^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Step 1

Simplify the numerator.

Apply the product rule to $25 x$ .

$\frac{25^{\frac{3}{2}} x^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{\frac{3}{2}} x^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5^{2 (\frac{3}{2})} x^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{3}{2})} x^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{5^{3} x^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Raise $5$ to the power of $3$ .

$\frac{125 x^{\frac{3}{2}}}{5 \cdot x^{\frac{1}{2}}}$

Step 2

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{125 x^{\frac{3}{2}} x^{- \frac{1}{2}}}{5}$

Step 3

Simplify the numerator.

Multiply $x^{\frac{3}{2}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Move $x^{- \frac{1}{2}}$ .

$\frac{125 (x^{- \frac{1}{2}} x^{\frac{3}{2}})}{5}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{125 x^{- \frac{1}{2} + \frac{3}{2}}}{5}$

Combine the numerators over the common denominator.

$\frac{125 x^{\frac{- 1 + 3}{2}}}{5}$

Add $- 1$ and $3$ .

$\frac{125 x^{\frac{2}{2}}}{5}$

Divide $2$ by $2$ .

$\frac{125 x^{1}}{5}$

Simplify $125 x^{1}$ .

$\frac{125 x}{5}$

Step 4

Cancel the common factor of $125$ and $5$ .

Factor $5$ out of $125 x$ .

$\frac{5 (25 x)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$\frac{5 (25 x)}{5 (1)}$

Cancel the common factor.

$\frac{5 (25 x)}{5 \cdot 1}$

Rewrite the expression.

$\frac{25 x}{1}$

Divide $25 x$ by $1$ .

$25 x$

Simplify ((25x)^(3/2))/(5*x^(1/2))

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