Which is an equivalent expression using a positive exponent?

To simplify the expression ((3/5)^{-8} ÷ (3/5)^{-4}), we can use the property of exponents that states (a^{-m} ÷ a^{-n} = a^{n-m}).

So, we have:

[

(3/5)^{-8} ÷ (3/5)^{-4} = (3/5)^{-8 – (-4)} = (3/5)^{-8 + 4} = (3/5)^{-4}

]

Now, to express it with a positive exponent, we can use the rule (a^{-m} = 1/a^{m}):

[

(3/5)^{-4} = frac{1}{(3/5)^{4}} = (5/3)^{4}

]

Thus, the equivalent expression using a positive exponent is ((5/3)^{4}).

The correct answer is ((5/3)^{4}).

To simplify the expression ((frac{3}{5})^{-8} div (frac{3}{5})^{-4}), we apply the property of exponents which states that (a^{-m} = frac{1}{a^m}) and also the rule for dividing exponents: (a^m div a^n = a^{m-n}).

1. Rewrite the expression as:

[

(frac{3}{5})^{-8} div (frac{3}{5})^{-4} = (frac{3}{5})^{-8 – (-4)} = (frac{3}{5})^{-8 + 4} = (frac{3}{5})^{-4}

]

2. Convert the negative exponent to a positive one:

[

(frac{3}{5})^{-4} = frac{1}{(frac{3}{5})^4} = (frac{5}{3})^{4}

]

Thus, the equivalent expression using a positive exponent is ((frac{5}{3})^{4}).

The correct answer is ((5/3)^{4}).