Cube of -343

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because multiplying a negative number by itself three times results in a negative number. The cube of -343 can be written as (-343)^3, which is the exponential form. Or it can also be written in arithmetic form as, (-343) × (-343) × (-343).

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, factor formula (a^3), or by using a calculator. These methods will help to cube the numbers faster and easier without confusion or getting stuck while evaluating the answers. By Multiplication Method Using a Formula Using a Calculator

The multiplication method is a process in mathematics used to find the product of numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts. Step 1: Write down the cube of the given number. \(-343)^3 = (-343) × (-343) × (-343)\) Step 2: You get -40,353,607 as the answer. Hence, the cube of -343 is -40,353,607.

The formula (a + b)^3 is a binomial formula for finding the cube of a number. The formula is expanded as a^3 + 3a^2b + 3ab^2 + b^3. Step 1: Split the number -343 into two parts, as -300 and -43. Let a = -300 and b = -43, so a + b = -343. Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. Step 3: Calculate each term: a^3 = (-300)^3 3a^2b = 3 × (-300)^2 × (-43) 3ab^2 = 3 × (-300) × (-43)^2 b^3 = (-43)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-300 - 43)^3 = (-300)^3 + 3 × (-300)^2 × (-43) + 3 × (-300) × (-43)^2 + (-43)^3 (-343)^3 = -27,000,000 + 11,070,000 + 1,656,900 - 79,507 (-343)^3 = -40,353,607 Step 5: Hence, the cube of -343 is -40,353,607.

To find the cube of -343 using a calculator, input the number -343 and use the cube function (if available) or multiply (-343) × (-343) × (-343). This operation calculates the value of (-343)^3, resulting in -40,353,607. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -343 Step 3: If the calculator has a cube function, press it to calculate (-343)^3. Step 4: If there is no cube function on the calculator, simply multiply -343 three times manually. Step 5: The calculator will display -40,353,607.

The cube of any even number is always even, while the cube of any odd number is always odd. The product of two or more perfect cube numbers is always a perfect cube. A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)^n, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number. Cube of a Number: Multiplying a number by itself three times is called the cube of a number. Exponential Form: A way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2^3 represents 2 × 2 × 2 equals 8. Perfect Cube: A number that is the cube of an integer. For example, 8 is a perfect cube because it can be expressed as 2^3. Cube Root: A number that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.