Exponents and Powers. The Small Numbers That Make a Big Impact. IntroductionExponents and powers are mathematical concepts that involve repeated multiplication. They are used to express large or small numbers in a more concise form. Understanding exponents and powers is essential for various fields, including science, engineering, and finance.What are Exponents and Powers?An exponent is a small number written above a base number. It indicates how many times the base number should be multiplied by itself. The base number raised to an exponent is called a power.The difference between Exponents and Powers is that an Exponent is the number indicating the number of times the base is multiplied, while a Power is the actual value resulting from the multiplication.Example:[latex]2^{3}[/latex] (read as "two to the power of three") means 2 multiplied by itself three times: [latex]2 × 2 × 2 = 8[/latex].Properties of ExponentsProduct of Powers Property: When multiplying powers with the same base, add the exponents. For example, [latex]2^{3} × 2^{4} = 2^{(3+4)} = 2^{7}[/latex].Quotient of Powers Property: When dividing powers with the same base, subtract the exponents. For example, [latex]2^{5} ÷ 2^{2} = 2^{(5-2)} = 2^{3}[/latex].Power of a Power Property: When raising a power to another power, multiply the exponents. For example, [latex](2^{3})^{4} = 2^{(3×4)} = 2^{12}[/latex].Zero Exponent Property: Any number raised to the power of 0 equals 1. For example, [latex]5^{0} = 1[/latex].Negative Exponent Property: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent. For example, [latex]2^{-3} = frac{1}{2^{3}}[/latex].Examples:Simplify: [latex]{(3^2)}^{4} = 3^{(2×4)} = 3^{8} = 6561[/latex].Evaluate: [latex]5^{-2} = frac{1}{5^{2}} = frac{1}{25}[/latex].Solve: [latex]2^{x} = 16[/latex]. Since [latex]2^{4} = 16[/latex], [latex]x = 4[/latex].Real-World ApplicationsExponents and powers are used in various fields, including:Science: Describing exponential growth and decay (e.g., population growth, radioactive decay).Finance: Calculating compound interest and inflation rates.Computer science: Representing large or small numbers in binary format.Engineering: Designing structures and analyzing systems.ConclusionExponents and powers are a fundamental concept in mathematics that allow us to express and manipulate numbers efficiently. Understanding the properties of exponents and their applications is essential for success in various fields.EXERCISE 7.0.What is the base in the expression [latex]5^{3}[/latex]?What does the exponent [latex]4[/latex] in the expression [latex]2^{4}[/latex] mean?Explain the difference between [latex]2^{3}[/latex] and [latex]3^{2}[/latex].What is the result of raising any number to the power of [latex]0[/latex]?Evaluate the expression [latex]4^{2}+3^{2} [/latex].Simplify the expression [latex](2^{5}div2^{2})times2^{3} [/latex].Why is it important to follow the order of operations when dealing with exponents?How can you use exponents to represent repeated multiplication?Create your own expression that involves exponents and requires multiple operations.Write a word problem that can be solved using exponents.Evaluate the expression [latex]-2^{5}[/latex]. What is the significance of the negative sign?Which is greater: [latex]2^{3}[/latex] or [latex]3^{2}[/latex]. Justify your answer.FOR MORE CONTENT!!!Register HERE Now! Pick a course, watch our Videos and take our CBT's.Additional Resources:N/A: https://www.waokmath.com[Image Source]: https://www.freepik.com/
