Simplify 8^(-1/4)*2^(-1/4)

$8^{- \frac{1}{4}} \cdot 2^{- \frac{1}{4}}$

Step 1

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

$\frac{1}{8^{\frac{1}{4}}} \cdot 2^{- \frac{1}{4}}$

Step 2

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

$\frac{1}{8^{\frac{1}{4}}} \cdot \frac{1}{2^{\frac{1}{4}}}$

Step 3

Combine fractions.

Combine.

$\frac{1 \cdot 1}{8^{\frac{1}{4}} \cdot 2^{\frac{1}{4}}}$

Multiply $1$ by $1$ .

$\frac{1}{8^{\frac{1}{4}} \cdot 2^{\frac{1}{4}}}$

Step 4

Simplify the denominator.

Rewrite $8$ as $2^{3}$ .

$\frac{1}{{(2^{3})}^{\frac{1}{4}} \cdot 2^{\frac{1}{4}}}$

Multiply the exponents in ${(2^{3})}^{\frac{1}{4}}$ .

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

$\frac{1}{2^{3 (\frac{1}{4})} \cdot 2^{\frac{1}{4}}}$

Combine $3$ and $\frac{1}{4}$ .

$\frac{1}{2^{\frac{3}{4}} \cdot 2^{\frac{1}{4}}}$

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

$\frac{1}{2^{\frac{3}{4} + \frac{1}{4}}}$

Combine the numerators over the common denominator.

$\frac{1}{2^{\frac{3 + 1}{4}}}$

Add $3$ and $1$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Evaluate the exponent.

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$