Answer:
[tex]2*2^{-3} * 2^{-5} =\frac{1}{128}[/tex]
Step-by-step explanation:
Given
[tex]2*2^{-3} * 2^{-5}[/tex]
Required
Write as a fraction
To do this, Jordan has to apply the following rules
Negative Exponent rule:
[tex]a^{-m} = \frac{1}{a^m}[/tex]
So, the expression is:
[tex]2*2^{-3} * 2^{-5} = \frac{2}{2^3 * 2^5}[/tex]
To solve further, we apply the product rule of exponent
[tex]a^m * a^n = a^{m+n}[/tex]
So, the expression is:
[tex]2*2^{-3} * 2^{-5} =\frac{2}{2^{3+5}}[/tex]
[tex]2*2^{-3} * 2^{-5} =\frac{2}{2^8}[/tex]
Evaluate the exponents
[tex]2*2^{-3} * 2^{-5} =\frac{2}{256}[/tex]
Divide the numerator and denominator by 2
[tex]2*2^{-3} * 2^{-5} =\frac{2/2}{256/2}[/tex]
[tex]2*2^{-3} * 2^{-5} =\frac{1}{128}[/tex]
