What does 3^4x2^3x5^2/3^2x5x2^3 equal?
Using the method of sorting the bases and subtracting the exponents.
To simplify the expression 3^4x2^3x5^2 divided by 3^2x5x2^3, we can use the method of sorting the bases and subtracting the exponents. Let's break it down step by step:
1. Start by sorting the bases in alphabetical order. In this case, the bases are 2, 3, and 5.
2. Now let's subtract the exponents for each base.
For the base 2:
The exponent in the numerator is 3 and the exponent in the denominator is 3.
Therefore, the exponent for 2 is 3 - 3 = 0.
For the base 3:
The exponent in the numerator is 4 and the exponent in the denominator is 2.
Therefore, the exponent for 3 is 4 - 2 = 2.
For the base 5:
The exponent in the numerator is 2 and the exponent in the denominator is 1.
Therefore, the exponent for 5 is 2 - 1 = 1.
3. Now we can rewrite the expression with the simplified exponents:
2^0 x 3^2 x 5^1
4. Any number raised to the power of 0 is equal to 1. So, 2^0 is 1.
5. Simplifying further, we have:
1 x 3^2 x 5^1
6. Now we can calculate the final result:
1 x 3^2 x 5^1 = 1 x 9 x 5 = 45
Therefore, 3^4x2^3x5^2/3^2x5x2^3 equals 45.