If 1080= 2^x × 3^y × 5 ,then (x-y) is equal to
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Given the equation:

\[ 1080 = 2^x \times 3^y \times 5 \]

we need to find \(x - y\).

First, factorize 1080:

\[ 1080 = 108 \times 10 \]
\[ 1080 = 108 \times 2 \times 5 \]
\[ 108 = 12 \times 9 \]
\[ 12 = 2^2 \times 3 \]
\[ 9 = 3^2 \]

Thus,

\[ 108 = 2^2 \times 3^3 \]

Combining all the factors, we get:

\[ 1080 = 2^2 \times 3^3 \times 2 \times 5 \]

This simplifies to:

\[ 1080 = 2^3 \times 3^3 \times 5 \]

Comparing this with the given form \( 2^x \times 3^y \times 5 \), we have:

\[ x = 3 \]
\[ y = 3 \]

Therefore,

\[ x - y = 3 - 3 = 0 \]

So, \( x - y \) is equal to \( 0 \).

Would you like more details or have any questions?

Here are some related questions:
1. What is the prime factorization of 1080?
2. How do you factorize a number into its prime components?
3. What is the significance of the exponents in prime factorization?
4. Can you provide an example of a different number and its prime factorization?
5. How do you solve for variables in an equation involving prime factorization?
6. What is the role of prime factorization in solving algebraic equations?
7. How do you verify the prime factorization of a number?
8. Can prime factorization be used to simplify fractions?

**Tip:** When solving for variables in exponential equations, comparing the exponents of the same prime factors can simplify the problem.

Explore how to solve the problem involving the prime factorization of 1080 and comparing exponents. Understand the concepts of prime factorization and exponents with a detailed step-by-step solution. Suitable for students in Grades 7-9.

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