Algebra Examples

$\frac{a^{\frac{5}{4}} {(2 a^{\frac{3}{4}})}^{3}}{a^{\frac{1}{4}}}$

Step 1

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

$a^{\frac{5}{4}} {(2 a^{\frac{3}{4}})}^{3} a^{- \frac{1}{4}}$

Step 2

Multiply $a^{\frac{5}{4}}$ by $a^{- \frac{1}{4}}$ by adding the exponents.

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Step 2.1

Move $a^{- \frac{1}{4}}$ .

$a^{- \frac{1}{4}} a^{\frac{5}{4}} {(2 a^{\frac{3}{4}})}^{3}$

Step 2.2

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

$a^{- \frac{1}{4} + \frac{5}{4}} {(2 a^{\frac{3}{4}})}^{3}$

Step 2.3

Combine the numerators over the common denominator.

$a^{\frac{- 1 + 5}{4}} {(2 a^{\frac{3}{4}})}^{3}$

Step 2.4

Add $- 1$ and $5$ .

$a^{\frac{4}{4}} {(2 a^{\frac{3}{4}})}^{3}$

Step 2.5

Divide $4$ by $4$ .

$a^{1} {(2 a^{\frac{3}{4}})}^{3}$

Step 3

Simplify $a^{1} {(2 a^{\frac{3}{4}})}^{3}$ .

$a {(2 a^{\frac{3}{4}})}^{3}$

Step 4

Apply the product rule to $2 a^{\frac{3}{4}}$ .

$a (2^{3} {(a^{\frac{3}{4}})}^{3})$

Step 5

Rewrite using the commutative property of multiplication.

$2^{3} a {(a^{\frac{3}{4}})}^{3}$

Step 6

Raise $2$ to the power of $3$ .

$8 a {(a^{\frac{3}{4}})}^{3}$

Step 7

Multiply the exponents in ${(a^{\frac{3}{4}})}^{3}$ .

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Step 7.1

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

$8 a \cdot a^{\frac{3}{4} \cdot 3}$

Step 7.2

Multiply $\frac{3}{4} \cdot 3$ .

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Step 7.2.1

Combine $\frac{3}{4}$ and $3$ .

$8 a \cdot a^{\frac{3 \cdot 3}{4}}$

Step 7.2.2

Multiply $3$ by $3$ .

$8 a \cdot a^{\frac{9}{4}}$

Step 8

Multiply $a$ by $a^{\frac{9}{4}}$ by adding the exponents.

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Step 8.1

Move $a^{\frac{9}{4}}$ .

$8 (a^{\frac{9}{4}} a)$

Step 8.2

Multiply $a^{\frac{9}{4}}$ by $a$ .

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Step 8.2.1

Raise $a$ to the power of $1$ .

$8 (a^{\frac{9}{4}} a^{1})$

Step 8.2.2

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

$8 a^{\frac{9}{4} + 1}$

Step 8.3

Write $1$ as a fraction with a common denominator.

$8 a^{\frac{9}{4} + \frac{4}{4}}$

Step 8.4

Combine the numerators over the common denominator.

$8 a^{\frac{9 + 4}{4}}$

Step 8.5

Add $9$ and $4$ .

$8 a^{\frac{13}{4}}$