Question

Which expressions are equivalent to (2 Superscript 5 Baseline) Superscript negative 2? 2–10 and StartFraction 1 Over 20 EndFraction 2–10 and StartFraction 1 Over 1024 EndFraction 10–2 and StartFraction 1 Over 100 EndFraction 10–10 and StartFraction 1 Over 100 EndFraction

Answer 1

Answer:

$\frac{1}{2^{10}} \ and\ \frac{1}{1024}$

Step-by-step explanation:

Given

$(2^{5})^{-2}$

Required

Find the equivalent;

To find the equivalent of the given expression, we make use of laws of indices;

Using the following law of indices;

$(a^m)^n = a^{m*n}$

So;

$(2^{5})^{-2}$ becomes

$(2^{5})^{-2} = 2^{5*-2}$

$(2^{5})^{-2} = 2^{-10}$ ------------ This is one equivalent

Solving further;

Using the following law of indices;

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

So;

$(2^{5})^{-2} = 2^{-10}$ becomes

$(2^{5})^{-2} = \frac{1}{2^{10}}$

$2^10 = 1024$

Hence;

$(2^{5})^{-2} = \frac{1}{1024}$

Conclusively; the equivalents of $(2^{5})^{-2}$ are $\frac{1}{2^{10}} \ and\ \frac{1}{1024}$