Rewrite the following expression with positive exponents. (9xy)^-6/7
To rewrite the expression (9xy)^(-6/7) with positive exponents, we can apply the rule of negative exponents. According to this rule, if we have an expression raised to a negative exponent, we can move it to the denominator and change the sign of the exponent to positive.
Starting with (9xy)^(-6/7), we can rewrite it as 1 / (9xy)^(6/7). This step introduces the reciprocal (1/x) of the base (9xy), and the exponent becomes positive (6/7).
Now, to further simplify the expression, we can evaluate the exponent (6/7) on the base (9xy). We can do this by taking the 6th root of the base raised to the power of 7. In other words, we can rewrite (9xy)^(6/7) as ((9xy)^7)^(1/7) since raising a power to a fraction is equal to taking the root of that power.
By applying this simplification, we get 1 / ((9xy)^7)^(1/7). Now we have a power raised to another power, which allows us to cancel out the exponents by multiplying them together. This gives us 1 / (9^(7/7) * x^(7/7) * y^(7/7)).
Simplifying further, we have 1 / (9 * x * y), which is the final expression with positive exponents: 1 / (9xy).