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

Simplify each term.

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Step 1.1.1

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 1.1.2

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

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

Step 1.1.3

Move the negative in front of the fraction.

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Factor $4$ out of $24 t^{16} - 4$ .

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Step 1.4.1

Factor $4$ out of $24 t^{16}$ .

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

Step 1.4.2

Factor $4$ out of $- 4$ .

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

Step 1.4.3

Factor $4$ out of $4 (6 t^{16}) + 4 (- 1)$ .

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

Step 2

To write $6 t^{\frac{4 (6 t^{16} - 1)}{t^{16}}}$ as a fraction with a common denominator, multiply by $\frac{t^{8}}{t^{8}}$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Factor $2$ out of $2 + 6 t^{\frac{4 (6 t^{16} - 1)}{t^{16}}} t^{8}$ .

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Step 4.1.1

Factor $2$ out of $2$ .

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

Step 4.1.2

Factor $2$ out of $6 t^{\frac{4 (6 t^{16} - 1)}{t^{16}}} t^{8}$ .

$\frac{2 (1) + 2 (3 t^{\frac{4 (6 t^{16} - 1)}{t^{16}}} t^{8})}{t^{8}}$

Step 4.1.3

Factor $2$ out of $2 (1) + 2 (3 t^{\frac{4 (6 t^{16} - 1)}{t^{16}}} t^{8})$ .

$\frac{2 (1 + 3 t^{\frac{4 (6 t^{16} - 1)}{t^{16}}} t^{8})}{t^{8}}$

Step 4.2

Multiply $t^{\frac{4 (6 t^{16} - 1)}{t^{16}}}$ by $t^{8}$ by adding the exponents.

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Step 4.2.1

Move $t^{8}$ .

$\frac{2 (1 + 3 (t^{8} t^{\frac{4 (6 t^{16} - 1)}{t^{16}}}))}{t^{8}}$

Step 4.2.2

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

$\frac{2 (1 + 3 t^{8 + \frac{4 (6 t^{16} - 1)}{t^{16}}})}{t^{8}}$

Step 4.2.3

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

$\frac{2 (1 + 3 t^{\frac{8 t^{16}}{t^{16}} + \frac{4 (6 t^{16} - 1)}{t^{16}}})}{t^{8}}$

Step 4.2.4

Combine the numerators over the common denominator.

$\frac{2 (1 + 3 t^{\frac{8 t^{16} + 4 (6 t^{16} - 1)}{t^{16}}})}{t^{8}}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Factor $4$ out of $8 t^{16} + 4 (6 t^{16} - 1)$ .

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Step 4.2.5.1.1

Factor $4$ out of $8 t^{16}$ .

$\frac{2 (1 + 3 t^{\frac{4 (2 t^{16}) + 4 (6 t^{16} - 1)}{t^{16}}})}{t^{8}}$

Step 4.2.5.1.2

Factor $4$ out of $4 (2 t^{16}) + 4 (6 t^{16} - 1)$ .

$\frac{2 (1 + 3 t^{\frac{4 (2 t^{16} + 6 t^{16} - 1)}{t^{16}}})}{t^{8}}$

Step 4.2.5.2

Add $2 t^{16}$ and $6 t^{16}$ .

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