Basic Math Examples

$\frac{2}{t^{8}} + 6 t^{24 - 4 t^{- 16}}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{2}{t^{8}} + 6 t^{24 - 4 \frac{1}{t^{16}}}$

Step 1.2

Combine $- 4$ and $\frac{1}{t^{16}}$ .

$\frac{2}{t^{8}} + 6 t^{24 + \frac{- 4}{t^{16}}}$

Step 1.3

Move the negative in front of the fraction.

$\frac{2}{t^{8}} + 6 t^{24 - \frac{4}{t^{16}}}$

Step 2

To write $6 t^{24 - \frac{4}{t^{16}}}$ as a fraction with a common denominator, multiply by $\frac{t^{8}}{t^{8}}$ .

$\frac{2}{t^{8}} + \frac{6 t^{24 - \frac{4}{t^{16}}} t^{8}}{t^{8}}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 + 6 t^{24 - \frac{4}{t^{16}}} t^{8}}{t^{8}}$

Step 4

Rewrite $\frac{2 + 6 t^{24 - \frac{4}{t^{16}}} t^{8}}{t^{8}}$ in a factored form.

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Step 4.1

Factor $2$ out of $2 + 6 t^{24 - \frac{4}{t^{16}}} t^{8}$ .

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Step 4.1.1

Factor $2$ out of $2$ .

$\frac{2 (1) + 6 t^{24 - \frac{4}{t^{16}}} t^{8}}{t^{8}}$

Step 4.1.2

Factor $2$ out of $6 t^{24 - \frac{4}{t^{16}}} t^{8}$ .

$\frac{2 (1) + 2 (3 t^{24 - \frac{4}{t^{16}}} t^{8})}{t^{8}}$

Step 4.1.3

Factor $2$ out of $2 (1) + 2 (3 t^{24 - \frac{4}{t^{16}}} t^{8})$ .

$\frac{2 (1 + 3 t^{24 - \frac{4}{t^{16}}} t^{8})}{t^{8}}$

Step 4.2

Multiply $t^{24 - \frac{4}{t^{16}}}$ by $t^{8}$ by adding the exponents.

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Step 4.2.1

Move $t^{8}$ .

$\frac{2 (1 + 3 (t^{8} t^{24 - \frac{4}{t^{16}}}))}{t^{8}}$

Step 4.2.2

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

$\frac{2 (1 + 3 t^{8 + 24 - \frac{4}{t^{16}}})}{t^{8}}$

Step 4.2.3

Add $8$ and $24$ .

$\frac{2 (1 + 3 t^{32 - \frac{4}{t^{16}}})}{t^{8}}$