Calculus Examples

$y = 2^{5 (- 1)} \cdot 3^{4 {(- 1)}^{2}}$

Step 1

Multiply $5$ by $- 1$ .

$y = 2^{- 5} \cdot 3^{4 {(- 1)}^{2}}$

Step 2

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

$y = \frac{1}{2^{5}} \cdot 3^{4 {(- 1)}^{2}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $2$ to the power of $5$ .

$y = \frac{1}{32} \cdot 3^{4 {(- 1)}^{2}}$

Step 3.2

Raise $- 1$ to the power of $2$ .

$y = \frac{1}{32} \cdot 3^{4 \cdot 1}$

Step 3.3

Multiply $4$ by $1$ .

$y = \frac{1}{32} \cdot 3^{4}$

Step 3.4

Raise $3$ to the power of $4$ .

$y = \frac{1}{32} \cdot 81$

Step 4

Combine $\frac{1}{32}$ and $81$ .

$y = \frac{81}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{81}{32}$

Decimal Form:

$y = 2.53125$

Mixed Number Form:

$y = 2 \frac{17}{32}$