To find the value of 16 raised to the power of 14, we start by expressing 16 as a power of 2. This can be done because 16 is equal to 2^4. Using this representation, we can rewrite the expression: 1614 = (24)14 Next, according to the laws of exponents, when you raise a power … Read more
To convert the improper fraction 23/7 into a mixed number, you need to follow these simple steps: Divide the numerator by the denominator: Start by performing the division of 23 by 7. When you divide, you find that 23 ÷ 7 = 3 with a remainder of 2. Identify the whole number: The quotient from … Read more
Determining whether a number is divisible by 3 is a simple process based on the sum of its digits. Here’s how you can do it: Identify the Number: Start with the number you want to check. For example, let’s take the number 123. Sum the Digits: Next, add together all the individual digits of that … Read more
Understanding Exponentiation Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In this case, you are asking about 8 to the power of 2 to the power of 3, which can also be expressed as 8^(2^3). To break this down, we need to follow the order of operations. Step 1: Calculate … Read more
To calculate 64 raised to the power of 13, we can first express 64 in exponential form. Since 64 is equal to 2 to the power of 6, we have: 64 = 26 Thus, 6413 can be rewritten as: (26)13 Using the property of exponents that states (am)n = am*n, we can simplify as follows: … Read more
Calculating 20% of 10,000 is a straightforward process. To determine this, you can follow these steps: First, understand that ‘percent’ means ‘per hundred.’ So, 20% can be expressed as the fraction 20/100 or as a decimal 0.20. Next, multiply the total amount (10,000) by the decimal equivalent of the percentage: Calculation: 20% of 10,000 = … Read more
The expression 9 to the power of 5 can be mathematically represented as 95. This means that you multiply 9 by itself a total of 5 times. Let’s break this down: 9 × 9 = 81 81 × 9 = 729 729 × 9 = 6,561 6,561 × 9 = 59,049 So, when you calculate … Read more
The least common multiple (LCM) of the first ten natural numbers (1 through 10) is a key concept in number theory and has many practical applications in mathematics. To find the LCM, we need to determine the smallest number that is a multiple of all these integers. First, let’s list the natural numbers we need … Read more
The equation you provided is a quadratic equation in the standard form of ax² + bx + c = 0. Here, a = 1, b = -5, and c = 1. To find the solution set of this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) … Read more
To convert the whole number 175 into a mixed number, we need to understand what a mixed number is. A mixed number consists of a whole part and a fractional part. In this case, since 175 is already a whole number, it can be expressed as a mixed number with 175 as the whole part … Read more