zoedaejohnson

04.06.2020 •

Mathematics

What characteristic do you look for in the table in order to decide whether the relationship is proportional?

What characteristic do you look for in the table in order to decide whether the relationship is pro

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Ответ:

zacharycheyne

18.03.2022

Mathematics

Question:

Which is the value of the expression

$\frac{(10^4)(5^2)}{(10^3)(5^3)}$

A. 1

B. 2

C. 8

D. 10

B. 2

Step-by-step explanation:

Given

$\frac{(10^4)(5^2)}{(10^3)(5^3)}$

Required

Evaluate

$\frac{(10^4)(5^2)}{(10^3)(5^3)}$

Split Fraction

$\frac{10^4}{10^3} * \frac{5^2}{5^3}$

From Laws of Indices

$\frac{a^x}{a^y} = a^{x-y}$

Applying this law to the above expression, we have

$10^{4-3} * 5^{2-3}$

$10^{1} * 5^{-1}$

$10 * 5^{-1}$

Also, from Laws of Indices

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

Applying this law to the above expression, we have

$10 * \frac{1}{5}$

Multiply 10 by 1

$\frac{10 * 1}{5}$

$\frac{10}{5}$

Hence,

$\frac{(10^4)(5^2)}{(10^3)(5^3)} = 2$

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