Question

simplify.
$128^{-\frac{3}{4}} cdot 2^{-\frac{3}{4}}$

Explanation:

Step1: Rewrite 128 as power of 2

$128 = 2^7$

Step2: Substitute into original expression

$2^{7 \times -\frac{3}{4}} \cdot 2^{-\frac{3}{4}}$

Step3: Simplify the first exponent

$2^{-\frac{21}{4}} \cdot 2^{-\frac{3}{4}}$

Step4: Add exponents (same base)

$2^{-\frac{21}{4} + (-\frac{3}{4})} = 2^{-\frac{24}{4}}$

Step5: Simplify the final exponent

$2^{-6} = \frac{1}{2^6}$

Step6: Calculate the denominator

$\frac{1}{64}$

Answer:

$\frac{1}{64}$