Basic Math Examples

$\frac{p^{\frac{1}{7}} p^{\frac{9}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 1

Multiply $p^{\frac{1}{7}}$ by $p^{\frac{9}{14}}$ by adding the exponents.

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Step 1.1

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

$\frac{p^{\frac{1}{7} + \frac{9}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 1.2

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{p^{\frac{1}{7} \cdot \frac{2}{2} + \frac{9}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 1.3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{7}$ by $\frac{2}{2}$ .

$\frac{p^{\frac{2}{7 \cdot 2} + \frac{9}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 1.3.2

Multiply $7$ by $2$ .

$\frac{p^{\frac{2}{14} + \frac{9}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{p^{\frac{2 + 9}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 1.5

Add $2$ and $9$ .

$\frac{p^{\frac{11}{14}} p^{\frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2

Multiply $p^{\frac{11}{14}}$ by $p^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1

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

$\frac{p^{\frac{11}{14} + \frac{1}{2}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{p^{\frac{11}{14} + \frac{1}{2} \cdot \frac{7}{7}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$\frac{p^{\frac{11}{14} + \frac{7}{2 \cdot 7}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.3.2

Multiply $2$ by $7$ .

$\frac{p^{\frac{11}{14} + \frac{7}{14}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{p^{\frac{11 + 7}{14}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.5

Add $11$ and $7$ .

$\frac{p^{\frac{18}{14}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.6

Cancel the common factor of $18$ and $14$ .

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Step 2.6.1

Factor $2$ out of $18$ .

$\frac{p^{\frac{2 (9)}{14}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $2$ out of $14$ .

$\frac{p^{\frac{2 \cdot 9}{2 \cdot 7}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.6.2.2

Cancel the common factor.

$\frac{p^{\frac{2 \cdot 9}{2 \cdot 7}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 2.6.2.3

Rewrite the expression.

$\frac{p^{\frac{9}{7}}}{{(p^{26})}^{\frac{- 1}{7}}}$

Step 3

Move ${(p^{26})}^{\frac{- 1}{7}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$p^{\frac{9}{7}} {(p^{26})}^{- \frac{- 1}{7}}$

Step 4

Multiply the exponents in ${(p^{26})}^{- \frac{- 1}{7}}$ .

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Step 4.1

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

$p^{\frac{9}{7}} p^{26 (- \frac{- 1}{7})}$

Step 4.2

Move the negative in front of the fraction.

$p^{\frac{9}{7}} p^{26 (- - \frac{1}{7})}$

Step 4.3

Multiply $- - \frac{1}{7}$ .

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Step 4.3.1

Multiply $- 1$ by $- 1$ .

$p^{\frac{9}{7}} p^{26 (1 (\frac{1}{7}))}$

Step 4.3.2

Multiply $\frac{1}{7}$ by $1$ .

$p^{\frac{9}{7}} p^{26 (\frac{1}{7})}$

Step 4.4

Combine $26$ and $\frac{1}{7}$ .

$p^{\frac{9}{7}} p^{\frac{26}{7}}$

Step 5

Multiply $p^{\frac{9}{7}}$ by $p^{\frac{26}{7}}$ by adding the exponents.

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Step 5.1

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

$p^{\frac{9}{7} + \frac{26}{7}}$

Step 5.2

Combine the numerators over the common denominator.

$p^{\frac{9 + 26}{7}}$

Step 5.3

Add $9$ and $26$ .

$p^{\frac{35}{7}}$

Step 5.4

Divide $35$ by $7$ .

$p^{5}$