Algebra Examples

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

Step 1

Multiply $s$ by $s$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $s$ .

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

Step 1.2

Multiply $s$ by $s$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Move $s^{\frac{1}{2}}$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine $2$ and $\frac{2}{2}$ .

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $2$ by $2$ .

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

Step 2.6.2

Add $1$ and $4$ .

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

Step 3

Multiply $x^{\frac{1}{2}}$ by $x^{8}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $x^{8}$ .

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

Step 3.2

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

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

Step 3.3

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.4

Combine $8$ and $\frac{2}{2}$ .

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Simplify the numerator.

Tap for more steps...

Step 3.6.1

Multiply $8$ by $2$ .

${(s^{\frac{5}{2}} x^{\frac{16 + 1}{2}})}^{8}$

Step 3.6.2

Add $16$ and $1$ .

${(s^{\frac{5}{2}} x^{\frac{17}{2}})}^{8}$

Step 4

Apply the product rule to $s^{\frac{5}{2}} x^{\frac{17}{2}}$ .

${(s^{\frac{5}{2}})}^{8} {(x^{\frac{17}{2}})}^{8}$

Step 5

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

Tap for more steps...

Step 5.1

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

$s^{\frac{5}{2} \cdot 8} {(x^{\frac{17}{2}})}^{8}$

Step 5.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1

Factor $2$ out of $8$ .

$s^{\frac{5}{2} \cdot (2 (4))} {(x^{\frac{17}{2}})}^{8}$

Step 5.2.2

Cancel the common factor.

$s^{\frac{5}{2} \cdot (2 \cdot 4)} {(x^{\frac{17}{2}})}^{8}$

Step 5.2.3

Rewrite the expression.

$s^{5 \cdot 4} {(x^{\frac{17}{2}})}^{8}$

Step 5.3

Multiply $5$ by $4$ .

$s^{20} {(x^{\frac{17}{2}})}^{8}$

Step 6

Multiply the exponents in ${(x^{\frac{17}{2}})}^{8}$ .

Tap for more steps...

Step 6.1

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

$s^{20} x^{\frac{17}{2} \cdot 8}$

Step 6.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.1

Factor $2$ out of $8$ .

$s^{20} x^{\frac{17}{2} \cdot (2 (4))}$

Step 6.2.2

Cancel the common factor.

$s^{20} x^{\frac{17}{2} \cdot (2 \cdot 4)}$

Step 6.2.3

Rewrite the expression.

$s^{20} x^{17 \cdot 4}$

Step 6.3

Multiply $17$ by $4$ .

$s^{20} x^{68}$