aromesburg

28.05.2021 •

Mathematics

A rectangle has a length that is 5 cm longer than its width. The perimeter of the rectangle is 180 cm. Find the length and the width

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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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