Use the laws of exponents to simplify
5/(6^12) 2/9 =
I am not sure how to do this at all. Please and Thank you
To simplify the expression using the laws of exponents, we need to understand two important rules: the rule of multiplication and the rule of division for exponents.
The rule of multiplication states that when multiplying two terms with the same base, we add the exponents. In other words:
a^m * a^n = a^(m + n)
The rule of division states that when dividing two terms with the same base, we subtract the exponents. In other words:
a^m / a^n = a^(m - n)
Now let's simplify the expression step by step:
1. Start by simplifying the numerator: 5/(6^12) = 5/6^12
2. Now apply the multiplication rule to the denominator: 2/9 = 2 * (1/9) = 2 * 9^-1
3. Apply the division rule to combine the denominator expressions: 5/6^12 * 2 * 9^-1 = 5/6^12 * 2 / 9^1
4. Apply the multiplication rule to combine the denominator expressions: 5/6^12 * 2 / 9^1 = 5/(6^12 * 9^1 * 2)
5. Simplify the denominator using the multiplication rule: 6^12 * 9^1 * 2 = (6 * 9)^(12 + 1) * 2 = 54^13 * 2
6. Substitute back the simplified denominator: 5/(6^12 * 9^1 * 2) = 5/(54^13 * 2)
Therefore, the simplified expression is 5/(54^13 * 2).