Problem 5 - Algebra 1: Concepts and Skills

Question

Match the power with the words that describe it. $$ 3^{7} $$ A. four to the sixth power B. three to the seventh power C. seven to the third power D. six to the fourth power

Step-by-Step Solution

Answer

The correct match for this power notation is option B, 'three to the seventh power'.

Step 1: Identify Notation

Firstly, identify and understand the given power notation. Here, \(3^{7}\) means 3 to the power of 7.

Step 2: Match Notation with Phrases

Afterwards, match the notation with the provided phrases. Since the base number is 3 and the power number is 7, the appropriate match is the phrase that has 'three' as a base and 'seven' as a power.

Step 3: Identify Correct Phrase

Lastly, identify the accurate match for this notation among four provided phrases. The phrase 'three to the seventh power' matches perfectly, which is option B.

Key Concepts

Exponents

Exponents are a way to express repeated multiplication of a number by itself. In mathematical terms, an exponent tells us how many times to multiply a base number by itself. For example, when we see the power notation like \(3^{7}\), it indicates that the number 3 is multiplied by itself 7 times: \(3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3\).

This notation is efficient and compact, making it easier to handle large numbers without writing long multiplication strings. Understanding how to read and interpret exponents is crucial, as they are fundamental components of mathematical expressions, and they appear in various fields of study including science, finance, and technology.

Basic Algebra

Basic algebra is a segment of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. The principles of algebra are applied when we manipulate expressions and equations to find the values of unknowns. In our textbook exercise, identifying the notation,\(3^{7}\), as 'three to the seventh power' involves the basic algebra skill of understanding power notation.

Algebra is the backbone of more complex mathematics and crucial for problem-solving across several disciplines. Clear knowledge of algebra basics is important for students as algebraic concepts are not only essentials in higher mathematics but are also applied in many real-world situations.

Mathematical Expressions

A mathematical expression is a combination of numbers, variables, and operation symbols that stands for a particular quantity. Unlike equations, expressions do not have an equals sign. In the context of our original exercise, \(3^{7}\) is an expression that uses the exponent to succinctly represent a larger calculation.

Mathematical expressions are essential in conveying ideas succinctly in mathematics and science. Students learn to perform operations with expressions, which may include simplification, factorization, or evaluation. Mastering expressions and the different ways they can be manipulated is fundamental for advancing in mathematics.