Simplify (x^(5/4)(x^4)^(1/8))/(x^(3/4))

$\frac{x^{\frac{5}{4}} {(x^{4})}^{\frac{1}{8}}}{x^{\frac{3}{4}}}$

Step 1

Move $x^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{5}{4}} {(x^{4})}^{\frac{1}{8}} x^{- \frac{3}{4}}$

Step 2

Multiply $x^{\frac{5}{4}}$ by $x^{- \frac{3}{4}}$ by adding the exponents.

Move $x^{- \frac{3}{4}}$ .

$x^{- \frac{3}{4}} x^{\frac{5}{4}} {(x^{4})}^{\frac{1}{8}}$

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

$x^{- \frac{3}{4} + \frac{5}{4}} {(x^{4})}^{\frac{1}{8}}$

Combine the numerators over the common denominator.

$x^{\frac{- 3 + 5}{4}} {(x^{4})}^{\frac{1}{8}}$

Add $- 3$ and $5$ .

$x^{\frac{2}{4}} {(x^{4})}^{\frac{1}{8}}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x^{\frac{2 (1)}{4}} {(x^{4})}^{\frac{1}{8}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x^{\frac{2 \cdot 1}{2 \cdot 2}} {(x^{4})}^{\frac{1}{8}}$

Cancel the common factor.

$x^{\frac{2 \cdot 1}{2 \cdot 2}} {(x^{4})}^{\frac{1}{8}}$

Rewrite the expression.

$x^{\frac{1}{2}} {(x^{4})}^{\frac{1}{8}}$

Step 3

Multiply the exponents in ${(x^{4})}^{\frac{1}{8}}$ .

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

$x^{\frac{1}{2}} x^{4 (\frac{1}{8})}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x^{\frac{1}{2}} x^{4 \frac{1}{4 (2)}}$

Cancel the common factor.

$x^{\frac{1}{2}} x^{4 \frac{1}{4 \cdot 2}}$

Rewrite the expression.

$x^{\frac{1}{2}} x^{\frac{1}{2}}$

Step 4

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

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

$x^{\frac{1}{2} + \frac{1}{2}}$

Combine the numerators over the common denominator.

$x^{\frac{1 + 1}{2}}$

Add $1$ and $1$ .

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

Divide $2$ by $2$ .

$x^{1}$

Step 5

Simplify $x^{1}$ .

$x$

Simplify (x^(5/4)(x^4)^(1/8))/(x^(3/4))

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