Simplify 4^(-7/4)*4^(-7/4)

$4^{- \frac{7}{4}} \cdot 4^{- \frac{7}{4}}$

Step 1

Multiply $4^{- \frac{7}{4}}$ by $4^{- \frac{7}{4}}$ by adding the exponents.

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

$4^{- \frac{7}{4} - \frac{7}{4}}$

Combine the numerators over the common denominator.

$4^{\frac{- 7 - 7}{4}}$

Subtract $7$ from $- 7$ .

$4^{\frac{- 14}{4}}$

Cancel the common factor of $- 14$ and $4$ .

Factor $2$ out of $- 14$ .

$4^{\frac{2 (- 7)}{4}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$4^{\frac{2 \cdot - 7}{2 \cdot 2}}$

Cancel the common factor.

$4^{\frac{2 \cdot - 7}{2 \cdot 2}}$

Rewrite the expression.

$4^{\frac{- 7}{2}}$

Move the negative in front of the fraction.

$4^{- \frac{7}{2}}$

Step 2

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

$\frac{1}{4^{\frac{7}{2}}}$

Step 3

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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:

$0.0078125$