Problem 5 Divide. $$u^{4} \div u^{4}$$... [FREE SOLUTION]

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Chapter 3: Problem 5

Divide. $$u^{4} \div u^{4}$$

Short Answer

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Question: Simplify the expression $$u^4 \div u^4$$. Answer: 1

Step by step solution

Identify the bases and exponents

In the given expression, we have the same base, u, raised to the powers of 4 and 4: $$u^4 \div u^4$$

Apply the rule for exponents with the same base

According to the rule, when dividing expressions with the same base, we subtract the exponent of the divisor from the exponent of the dividend: $$u^{4-4}$$

Simplify the expression

Now subtract the exponents: $$u^0$$

Apply the rule for any base raised to a power of 0

Recall that any base raised to the power of 0 is equal to 1: $$1$$ So, $$u^4 \div u^4 = 1$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bases and Exponents

Understanding how bases and exponents work is essential in algebra. An exponent tells us how many times to multiply the base by itself. For instance, in the expression $ u^4 $, the base is $ u $ and the exponent is 4, indicating $ u $ should be multiplied by itself four times: $ u \times u \times u \times u $.

When we divide two powers with the same base, we use the rules for exponents to simplify the expression. The key rule that applies here is: when you divide powers with the same base, subtract the exponents. It comes from the fact that division is the inverse operation of multiplication.

Simplifying Expressions

Simplifying expressions is like tidying up the math world. It helps us make complicated things look much simpler! To simplify an expression with exponents, we follow certain rules that make our calculations easier. One of these rules we apply when dividing. It's a kind of 'short cut' that avoids having to expand out all the multiplications.

For example, $ u^4 \div u^4 $ simplifies by using the rule of exponents to subtract the powers. Our earlier steps showed this process, resulting in $ u^{4-4} $ which greatly simplifies our work. This step is crucial for ensuring that we can quickly and accurately simplify expressions involving division of exponents.

Zero Exponent Rule

The zero exponent rule is a fantastic shortcut in mathematics that can turn any daunting expression with a bunch of zeroes into a simple number 1. It states that any nonzero base raised to the power of 0 equals 1. This is because the pattern of dividing exponents leads to anything raised to the power of 0 being equal to 1.

This rule is pivotal in our exercise where after subtracting the exponents we get $ u^0 $, which according the zero exponent rule simplifies to 1. This concept not only simplifies calculations but also underpins many other mathematical theories and is a fundamental property of exponents.

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91影视

Divide. $$u^{4} \div u^{4}$$

Short Answer

Step by step solution

Identify the bases and exponents

Apply the rule for exponents with the same base

Simplify the expression

Apply the rule for any base raised to a power of 0

Key Concepts

Bases and Exponents

Simplifying Expressions

Zero Exponent Rule

One App. One Place for Learning.

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