Basic Math Examples

$\frac{s^{\frac{3}{4}} {(2 s^{\frac{5}{8}})}^{2}}{s^{\frac{1}{4}}}$

Step 1

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

$s^{\frac{3}{4}} {(2 s^{\frac{5}{8}})}^{2} s^{- \frac{1}{4}}$

Step 2

Multiply $s^{\frac{3}{4}}$ by $s^{- \frac{1}{4}}$ by adding the exponents.

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Step 2.1

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

$s^{- \frac{1}{4}} s^{\frac{3}{4}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.2

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

$s^{- \frac{1}{4} + \frac{3}{4}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.3

Combine the numerators over the common denominator.

$s^{\frac{- 1 + 3}{4}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.4

Add $- 1$ and $3$ .

$s^{\frac{2}{4}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.5

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

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Step 2.5.1

Factor $2$ out of $2$ .

$s^{\frac{2 (1)}{4}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $4$ .

$s^{\frac{2 \cdot 1}{2 \cdot 2}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.5.2.2

Cancel the common factor.

$s^{\frac{2 \cdot 1}{2 \cdot 2}} {(2 s^{\frac{5}{8}})}^{2}$

Step 2.5.2.3

Rewrite the expression.

$s^{\frac{1}{2}} {(2 s^{\frac{5}{8}})}^{2}$

Step 3

Apply the product rule to $2 s^{\frac{5}{8}}$ .

$s^{\frac{1}{2}} (2^{2} {(s^{\frac{5}{8}})}^{2})$

Step 4

Rewrite using the commutative property of multiplication.

$2^{2} s^{\frac{1}{2}} {(s^{\frac{5}{8}})}^{2}$

Step 5

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

$4 s^{\frac{1}{2}} {(s^{\frac{5}{8}})}^{2}$

Step 6

Multiply the exponents in ${(s^{\frac{5}{8}})}^{2}$ .

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Step 6.1

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

$4 s^{\frac{1}{2}} s^{\frac{5}{8} \cdot 2}$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Factor $2$ out of $8$ .

$4 s^{\frac{1}{2}} s^{\frac{5}{2 (4)} \cdot 2}$

Step 6.2.2

Cancel the common factor.

$4 s^{\frac{1}{2}} s^{\frac{5}{2 \cdot 4} \cdot 2}$

Step 6.2.3

Rewrite the expression.

$4 s^{\frac{1}{2}} s^{\frac{5}{4}}$

Step 7

Multiply $s^{\frac{1}{2}}$ by $s^{\frac{5}{4}}$ by adding the exponents.

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Step 7.1

Move $s^{\frac{5}{4}}$ .

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

Step 7.2

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

$4 s^{\frac{5}{4} + \frac{1}{2}}$

Step 7.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 s^{\frac{5}{4} + \frac{1}{2} \cdot \frac{2}{2}}$

Step 7.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.4.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$4 s^{\frac{5}{4} + \frac{2}{2 \cdot 2}}$

Step 7.4.2

Multiply $2$ by $2$ .

$4 s^{\frac{5}{4} + \frac{2}{4}}$

Step 7.5

Combine the numerators over the common denominator.

$4 s^{\frac{5 + 2}{4}}$

Step 7.6

Add $5$ and $2$ .

$4 s^{\frac{7}{4}}$