Calculus Examples

$(- 2 t^{- 3}) (3 t^{\frac{2}{3}})$

Step 1

Rewrite using the commutative property of multiplication.

$- 2 \cdot 3 t^{- 3} t^{\frac{2}{3}}$

Step 2

Multiply $t^{- 3}$ by $t^{\frac{2}{3}}$ by adding the exponents.

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Step 2.1

Move $t^{\frac{2}{3}}$ .

$- 2 \cdot 3 (t^{\frac{2}{3}} t^{- 3})$

Step 2.2

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

$- 2 \cdot 3 t^{\frac{2}{3} - 3}$

Step 2.3

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 2 \cdot 3 t^{\frac{2}{3} - 3 \cdot \frac{3}{3}}$

Step 2.4

Combine $- 3$ and $\frac{3}{3}$ .

$- 2 \cdot 3 t^{\frac{2}{3} + \frac{- 3 \cdot 3}{3}}$

Step 2.5

Combine the numerators over the common denominator.

$- 2 \cdot 3 t^{\frac{2 - 3 \cdot 3}{3}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 3$ by $3$ .

$- 2 \cdot 3 t^{\frac{2 - 9}{3}}$

Step 2.6.2

Subtract $9$ from $2$ .

$- 2 \cdot 3 t^{\frac{- 7}{3}}$

Step 2.7

Move the negative in front of the fraction.

$- 2 \cdot 3 t^{- \frac{7}{3}}$

Step 3

Multiply $- 2$ by $3$ .

$- 6 t^{- \frac{7}{3}}$

Step 4

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

$- 6 \frac{1}{t^{\frac{7}{3}}}$

Step 5

Combine $- 6$ and $\frac{1}{t^{\frac{7}{3}}}$ .

$\frac{- 6}{t^{\frac{7}{3}}}$

Step 6

Move the negative in front of the fraction.

$- \frac{6}{t^{\frac{7}{3}}}$