Question

Simplify each expression. $$ \left(\frac{2^{2}}{2^{3}}\right)^{5} $$

   Simplify each expression.
$$
\left(\frac{2^{2}}{2^{3}}\right)^{5}
$$

Algebra 1 Common Core

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 7, Problem 38

Instant Answer

Solved by Expert Lourence Gonhovi

03/31/2020

Step 1

Since the bases are the same (both are 2), we subtract the exponents. This gives us $2^{2-3}$ or $2^{-1}$. Show more…

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Simplify each expression. $$ \left(\frac{2^{2}}{2^{3}}\right)^{5} $$

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Key Concepts

Quotient Rule for Exponents

This rule states that when dividing two expressions with the same base, you subtract the exponent in the denominator from the exponent in the numerator. In general, for any nonzero base a, a^m / a^n equals a^(m - n).

Power of a Power Rule

This rule indicates that when an exponential expression is raised to another power, you multiply the exponents. That is, for any base a and exponents m and n, (a^m)^n equals a^(m*n).

Negative Exponent Concept

A negative exponent represents the reciprocal of the base raised to the corresponding positive exponent. For instance, a^-n is equivalent to 1/(a^n), which is important for expressing and simplifying results that have negative exponents.

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