Finite Math Examples

$m^{\frac{15}{16} \cdot (m^{- \frac{1}{2}} + 8 m)}$

Step 1

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

$m^{\frac{15}{16} \cdot (\frac{1}{m^{\frac{1}{2}}} + 8 m)}$

Step 2

Apply the distributive property.

$m^{\frac{15}{16} \cdot \frac{1}{m^{\frac{1}{2}}} + \frac{15}{16} (8 m)}$

Step 3

Combine.

$m^{\frac{15 \cdot 1}{16 m^{\frac{1}{2}}} + \frac{15}{16} (8 m)}$

Step 4

Cancel the common factor of $8$ .

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Step 4.1

Factor $8$ out of $16$ .

$m^{\frac{15 \cdot 1}{16 m^{\frac{1}{2}}} + \frac{15}{8 (2)} (8 m)}$

Step 4.2

Factor $8$ out of $8 m$ .

$m^{\frac{15 \cdot 1}{16 m^{\frac{1}{2}}} + \frac{15}{8 (2)} (8 (m))}$

Step 4.3

Cancel the common factor.

$m^{\frac{15 \cdot 1}{16 m^{\frac{1}{2}}} + \frac{15}{8 \cdot 2} (8 m)}$

Step 4.4

Rewrite the expression.

$m^{\frac{15 \cdot 1}{16 m^{\frac{1}{2}}} + \frac{15}{2} m}$

Step 5

Combine $\frac{15}{2}$ and $m$ .

$m^{\frac{15 \cdot 1}{16 m^{\frac{1}{2}}} + \frac{15 m}{2}}$

Step 6

Multiply $15$ by $1$ .

$m^{\frac{15}{16 m^{\frac{1}{2}}} + \frac{15 m}{2}}$