Express 256 × 243 in Exponential Form

Express 256 × 243 in Exponential Form

To express 256×243 in exponential form, you can break down each number into its prime factors and then combine them. We have the following set of options:

2⁸ x 3⁵

2⁷ x 3⁴

2⁶ x 3³

2² x 3²

Break down each number into its prime factors

256 = 2×2×2×2×2×2×2×2 = 2⁸

243 = 3×3×3×3×3 = 3⁵

Write the numbers in exponential form

256 in exponential form is 2⁸

243 in exponential form is 3⁵

Combine the exponential forms of the numbers

256 × 243 = 2⁸ x 3⁵

Therefore, the exponential form of 256 × 243 is 2⁸ x 3⁵

Exponential Form and Prime Factorization

Exponential form is a way to express numbers using powers or exponents. It involves writing a number as a base raised to a power, where the power represents the number of times the base is multiplied by itself.

Prime Factorization:

• To write a number in exponential form, you first break it down into its prime factors.
• Prime factors are the smallest prime numbers that multiply together to give the original number.

Writing in Exponential Form:

• Once you have the prime factorization of a number, you can express it in exponential form by writing the prime factors as a base raised to the appropriate power.
• Each prime factor appears as the base, and its exponent is the number of times that prime factor occurs in the prime factorization.

Multiplication in Exponential Form:

• When multiplying numbers in exponential form, you combine the bases if they are the same and add their exponents.
• This simplifies the expression and allows you to represent the result in exponential form as well.

Applications and Importance:

• Exponential form is widely used in mathematics, science, and engineering to represent large or small numbers efficiently.
• It helps in performing calculations involving repeated multiplication more easily and compactly.