Problem 5 - Algebra 1: Concepts and Skills

Question

Use the quotient of powers property to simplify the expression. $$ \frac{(-2)^{8}}{(-2)^{3}} $$

Step-by-Step Solution

Answer

-32

Step 1: Identify the parts of the formula

Identify the bases and the exponents in the given expression. Here, the base 'a' is -2, and the exponents 'm' and 'n' are 8 and 3 respectively. The given expression matches the form \(a^{m}/a^{n}\). Use the Quotient of Powers property to rewrite it.

Step 2: Apply the Quotient of Powers rule

According to the Quotient of Powers Property, you can subtract the exponent of the denominator from the exponent of the numerator if the bases are the same. So, rewrite \((-2)^8/(-2)^3\) as \[(-2)^{8-3}\].

Step 3: Simplify the exponent

Now subtract the exponents. 8 - 3 equals 5. So, \[(-2)^{8-3}\] simplifies to \[(-2)^5\].

Step 4: Calculate the value

Now just calculate the value of \(-2^5\). Since the base is a negative number and the exponent is odd, the result will be a negative number. Multiply -2 by itself 5 times to get -32.