Write the Fraction in Simplest Form ((2^2)÷(2^3))^7

${(2^{2} \div 2^{3})}^{7}$

Rewrite the division as a fraction.

${(\frac{2^{2}}{2^{3}})}^{7}$

Cancel the common factor of $2^{2}$ and $2^{3}$ .

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Multiply by $1$ .

${(\frac{2^{2} \cdot 1}{2^{3}})}^{7}$

Cancel the common factors.

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Factor $2^{2}$ out of $2^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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Apply the product rule to $\frac{1}{2}$ .

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

One to any power is one.

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

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

$\frac{1}{128}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{128}$

Decimal Form:

$0.0078125$

Write the Fraction in Simplest Form ((2^2)÷(2^3))^7

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