Finite Math Examples

$m^{\frac{13}{16}} (m^{\frac{- 1}{4}} + 5 m)$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$m^{\frac{13}{16}} (m^{- \frac{1}{4}} + 5 m)$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$m^{\frac{13}{16}} (\frac{1}{m^{\frac{1}{4}}} + 5 m)$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$m^{\frac{13}{16}} \frac{1}{m^{\frac{1}{4}}} + m^{\frac{13}{16}} (5 m)$

Step 2.2

Cancel the common factor of $m^{\frac{1}{4}}$ .

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Step 2.2.1

Factor $m^{\frac{1}{4}}$ out of $m^{\frac{13}{16}}$ .

$m^{\frac{1}{4}} m^{\frac{9}{16}} \frac{1}{m^{\frac{1}{4}}} + m^{\frac{13}{16}} (5 m)$

Step 2.2.2

Cancel the common factor.

$m^{\frac{1}{4}} m^{\frac{9}{16}} \frac{1}{m^{\frac{1}{4}}} + m^{\frac{13}{16}} (5 m)$

Step 2.2.3

Rewrite the expression.

$m^{\frac{9}{16}} + m^{\frac{13}{16}} (5 m)$

Step 2.3

Rewrite using the commutative property of multiplication.

$m^{\frac{9}{16}} + 5 m^{\frac{13}{16}} m$

Step 3

Multiply $m^{\frac{13}{16}}$ by $m$ by adding the exponents.

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Step 3.1

Move $m$ .

$m^{\frac{9}{16}} + 5 (m \cdot m^{\frac{13}{16}})$

Step 3.2

Multiply $m$ by $m^{\frac{13}{16}}$ .

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Step 3.2.1

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

$m^{\frac{9}{16}} + 5 (m^{1} m^{\frac{13}{16}})$

Step 3.2.2

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

$m^{\frac{9}{16}} + 5 m^{1 + \frac{13}{16}}$

Step 3.3

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

$m^{\frac{9}{16}} + 5 m^{\frac{16}{16} + \frac{13}{16}}$

Step 3.4

Combine the numerators over the common denominator.

$m^{\frac{9}{16}} + 5 m^{\frac{16 + 13}{16}}$

Step 3.5

Add $16$ and $13$ .

$m^{\frac{9}{16}} + 5 m^{\frac{29}{16}}$