Question

Jordan was given the expression 2x2^-3 x 2^-5 How should he write the expression as a fraction? Describe the exponent rules Jordan should use to simplify the expression

Answer 1

Answer:

$2*2^{-3} * 2^{-5} =\frac{1}{128}$

Step-by-step explanation:

Given

$2*2^{-3} * 2^{-5}$

Required

Write as a fraction

To do this, Jordan has to apply the following rules

Negative Exponent rule:

$a^{-m} = \frac{1}{a^m}$

So, the expression is:

$2*2^{-3} * 2^{-5} = \frac{2}{2^3 * 2^5}$

To solve further, we apply the product rule of exponent

$a^m * a^n = a^{m+n}$

So, the expression is:

$2*2^{-3} * 2^{-5} =\frac{2}{2^{3+5}}$

$2*2^{-3} * 2^{-5} =\frac{2}{2^8}$

Evaluate the exponents

$2*2^{-3} * 2^{-5} =\frac{2}{256}$

Divide the numerator and denominator by 2

$2*2^{-3} * 2^{-5} =\frac{2/2}{256/2}$

$2*2^{-3} * 2^{-5} =\frac{1}{128}$