/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 Write \(\frac{8^{1000}}{2^{5}}\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 21

Write \(\frac{8^{1000}}{2^{5}}\) as a power of 2 .

Short Answer

Expert verified
The simplified expression is \(2^{2995}\).

Step by step solution

01

Write the numerator as a power of 2

Observe that 8 is equal to 2 raised to the power of 3 (i.e., \(2^3\)). So, we can write \(8^{1000}\) as \((2^3)^{1000}\).
02

Simplify the exponent

Using the power of a power rule, \((a^m)^n = a^{mn}\), we have: \((2^3)^{1000} = 2^{3 \times 1000}\) or \(2^{3000}\).
03

Rewrite the expression as a power of 2

Now we can re-write the given expression as: \(\frac{2^{3000}}{2^5}\).
04

Simplify the expression using the rule of exponents

Using the quotient rule, \(\frac{a^m}{a^n} = a^{m-n}\), we have: \(\frac{2^{3000}}{2^5} = 2^{3000 - 5}\) or \(2^{2995}\). The given expression is equal to \(2^{2995}\) as a power of 2.

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