Cube of -64

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 -64 can be written as (-64)^3, which is the exponential form. Or it can also be written in arithmetic form as, -64 × -64 × -64.

In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a^3), or by using a calculator. These three methods will help individuals 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 numbers 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. (-64)^3 = -64 × -64 × -64 Step 2: You get -262,144 as the answer. Hence, the cube of -64 is -262,144.

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 -64 into two parts, as -60 and -4. Let a = -60 and b = -4, so a + b = -64 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-60)^3 3a^2b = 3 × (-60)^2 × (-4) 3ab^2 = 3 × (-60) × (-4)^2 b^3 = (-4)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-60 - 4)^3 = (-60)^3 + 3 × (-60)^2 × (-4) + 3 × (-60) × (-4)^2 + (-4)^3 (-64)^3 = -216,000 - 43,200 - 2,880 - 64 (-64)^3 = -262,144 Step 5: Hence, the cube of -64 is -262,144.

To find the cube of -64 using a calculator, input the number -64 and use the cube function (if available) or multiply -64 × -64 × -64. This operation calculates the value of (-64)^3, resulting in -262,144. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -64 Step 3: If the calculator has a cube function, press it to calculate (-64)^3. Step 4: If there is no cube function on the calculator, simply multiply -64 three times manually. Step 5: The calculator will display -262,144.

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.

1. 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. 2. Cube of a Number: Multiplying a number by itself three times is called the cube of a number. 3. 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. 4. Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself three times. 5. Cube Root: The number that, when multiplied by itself three times, gives the original number. For example, the cube root of -64 is -4.