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Chapter 0: Problem 126

Explain the quotient rule for exponents. Use \(\frac{5^{8}}{5^{2}}\) in your explanation.

Short Answer

Expert verified
Using the Quotient Rule for Exponents, \(\frac{5^{8}}{5^{2}}\) simplifies to \(5^{6}\).

Step by step solution

01

Understanding the Quotient Rule for Exponents

The Quotient Rule for Exponents states that when dividing like bases, subtract the exponents. In general terms, for any non-zero number a, it's: \(a^{m}/a^{n} = a^{m-n}\), where m and n are any real numbers.
02

Identify the Base and Exponents

For the expression \(\frac{5^{8}}{5^{2}}\), the base (a) is 5, the exponent in the numerator (m) is 8, and the exponent in the denominator (n) is 2.
03

Apply the Quotient Rule

Subtract the denominator's exponent from the numerator's exponent: \(5^{8-2} = 5^{6}\)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Special-product formulas have patterns that make their multiplications quicker than using the FOIL method.

Explain how to convert from decimal to scientific notation and give an example.

Factor completely. $$ x^{4}-y^{4}-2 x^{3} y+2 x y^{3} $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(x^{4}-16\) is factored completely as \(\left(x^{2}+4\right)\left(x^{2}-4\right)\)

Explain how to factor the difference of two squares. Provide an example with your explanation.
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