Use the properties of exponents to rewrite each expression so that it contains only positive exponents and simplify the result. The answer is suppose to be 1/9. thank you
(b^-1/3a^-1)(3a/b)^-1
To rewrite the expression using the properties of exponents and simplify it, let's break it down step by step:
1. Start with the expression: (b^(-1/3)a^(-1))(3a/b)^(-1)
2. First, let's bring the negative exponent of the second term, (3a/b)^(-1), to the numerator by reciprocating it: 1/(3a/b)
This becomes: (b^(-1/3)a^(-1))(b/(3a))
3. Next, let's simplify the expression by multiplying the coefficients and combining the variables with the same base:
a^(-1) * a = 1/a
b^(-1/3) * b = 1/b^(1/3), which simplifies to b^(-1/3)
Our expression now becomes: (1/a)(1/b^(1/3))(b/(3a))
4. Cancel out common factors. We can cancel out the 'a' term in the numerator and denominator:
(1 / a) * (b / (3a)) = b / (3a^2)
5. Simplify further by multiplying the coefficients:
b / (3a^2)
6. Finally, rearrange the expression to have positive exponents:
1 / (3a^2b)
Therefore, the simplified expression is 1 / (3a^2b). The answer is not 1/9 as mentioned in the question.
(1/b / 3/a)(b/3a)
(a/3b)(b/3a)
1/9