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Evaluate 2^2*2^-9

$2^{2} \cdot 2^{- 9}$

Step 1

Multiply $2^{2}$ by $2^{- 9}$ by adding the exponents.

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

$2^{2 - 9}$

Subtract $9$ from $2$ .

$2^{- 7}$

$2^{- 7}$

Step 2

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

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

Step 3

Raise $2$ to the power of $7$ .

$\frac{1}{128}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{128}$

Decimal Form:

$0.0078125$

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