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Chapter 0: Problem 90

Perform the indicated operation or operations. $$ \frac{(5 x-3)^{6}}{(5 x-3)^{4}} $$

Short Answer

Expert verified
The simplified form of \( \frac{(5x-3)^{6}}{(5x-3)^{4}} \) is \( (5x-3)^{2} \).

Step by step solution

01

Identify the Base and Exponents

The expression to be simplified is \( \frac{(5x-3)^{6}}{(5x-3)^{4}} \). In both the numerator and denominator, the base is the term (5x-3) and the exponents are 6 and 4 respectively.
02

Apply the Law of Exponents

Apply the law of exponents for division, which states that when dividing two exponential expressions that have the same base, subtract the exponent of the denominator from the exponent of the numerator. This yields \( (5x-3)^{6-4} \).
03

Simplify

By performing the subtraction in the exponent, the final simplified expression is \( (5x-3)^{2} \).

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Most popular questions from this chapter

Evaluate each expression without using a calculator. $$16^{-\frac{5}{2}}$$

Simplify by reducing the index of the radical. $$\sqrt[9]{x^{6}}$$

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

There are approximately \(3.2 \times 10^{7}\) seconds in a year. According to the United States Department of Agriculture, Americans consume 127 chickens per second. How many chickens are eaten per year in the United States? Express the answer in scientific notation.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$2 x^{4}\left(8 x^{4}+3 x\right)$$
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