Cube of -13

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 a negative number multiplied by itself three times results in a negative number. The cube of -13 can be written as (-13)^3, which is the exponential form. Or it can also be written in arithmetic form as, -13 × -13 × -13.

In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a^3), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or 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 two 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. (-13)^3 = -13 × -13 × -13 Step 2: You get -2,197 as the answer. Hence, the cube of -13 is -2,197.

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 -13 into two parts, as -10 and -3. Let a = -10 and b = -3, so a + b = -13 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-10)^3 3a^2b = 3 × (-10)^2 × -3 3ab^2 = 3 × -10 × (-3)^2 b^3 = (-3)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-10 + -3)^3 = (-10)^3 + 3 × (-10)^2 × -3 + 3 × -10 × (-3)^2 + (-3)^3 (-13)^3 = -1,000 - 900 + 270 - 27 (-13)^3 = -2,197 Step 5: Hence, the cube of -13 is -2,197.

To find the cube of -13 using a calculator, input the number -13 and use the cube function (if available) or multiply -13 × -13 × -13. This operation calculates the value of (-13)^3, resulting in -2,197. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press -1 followed by 3 Step 3: If the calculator has a cube function, press it to calculate (-13)^3. Step 4: If there is no cube function on the calculator, simply multiply -13 three times manually. Step 5: The calculator will display -2,197.

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 sum, 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. Negative Numbers: Numbers less than zero, often used to represent loss, deficiency, or opposite directions. Perfect Cube: A number that can be expressed as the cube of an integer.