Calculus Examples

$(t^{\frac{1}{7}}) (1 - \frac{1}{2} t^{- \frac{1}{2}})$

Step 1

Simplify each term.

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Step 1.1

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

$t^{\frac{1}{7}} (1 - \frac{1}{2} \cdot \frac{1}{t^{\frac{1}{2}}})$

Step 1.2

Multiply $\frac{1}{t^{\frac{1}{2}}}$ by $\frac{1}{2}$ .

$t^{\frac{1}{7}} (1 - \frac{1}{t^{\frac{1}{2}} \cdot 2})$

Step 1.3

Move $2$ to the left of $t^{\frac{1}{2}}$ .

$t^{\frac{1}{7}} (1 - \frac{1}{2 t^{\frac{1}{2}}})$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$t^{\frac{1}{7}} \cdot 1 + t^{\frac{1}{7}} (- \frac{1}{2 t^{\frac{1}{2}}})$

Step 2.2

Simplify the expression.

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Step 2.2.1

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

$t^{\frac{1}{7}} + t^{\frac{1}{7}} (- \frac{1}{2 t^{\frac{1}{2}}})$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$t^{\frac{1}{7}} - t^{\frac{1}{7}} \frac{1}{2 t^{\frac{1}{2}}}$

Step 2.3

Cancel the common factor of $t^{\frac{1}{7}}$ .

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Step 2.3.1

Factor $t^{\frac{1}{7}}$ out of $- t^{\frac{1}{7}}$ .

$t^{\frac{1}{7}} + t^{\frac{1}{7}} \cdot - 1 \frac{1}{2 t^{\frac{1}{2}}}$

Step 2.3.2

Factor $t^{\frac{1}{7}}$ out of $2 t^{\frac{1}{2}}$ .

$t^{\frac{1}{7}} + t^{\frac{1}{7}} \cdot - 1 \frac{1}{t^{\frac{1}{7}} (2 t^{\frac{5}{14}})}$

Step 2.3.3

Cancel the common factor.

$t^{\frac{1}{7}} + t^{\frac{1}{7}} \cdot - 1 \frac{1}{t^{\frac{1}{7}} (2 t^{\frac{5}{14}})}$

Step 2.3.4

Rewrite the expression.

$t^{\frac{1}{7}} - \frac{1}{2 t^{\frac{5}{14}}}$