Question

Rewrite using only positive rational exponents. (x⁴/⁹))⁵/⁷

Answer 1

To rewrite (x⁴/⁹))⁵/⁷ using positive rational exponents, we move the negative exponent to the denominator, change its sign to positive, and simplify the expression to 1/x⁹⁵/⁷.

Step-by-step explanation:

To rewrite the expression using only positive rational exponents, we need to convert the given expression, (x⁴/⁹))⁵/⁷, into a fractional form where the numerator and denominator have positive exponents.

First, let's rewrite the numerator. The numerator x⁴/⁹ has a negative exponent (-⁹), which means we can move it to the denominator and change the sign of the exponent to positive. So, x⁴/⁹ becomes 1/x⁹.

Next, let's rewrite the denominator. The denominator has a positive exponent (⁷), so we can leave it as is.

Now, let's substitute the rewritten numerator and denominator into the original expression: (1/x⁹)⁵/⁷. Since the exponent outside the parentheses applies to both the numerator and denominator, we can distribute it: 1⁵/x⁹⁵/⁷. Finally, we simplify further: 1⁵ is just 1, so the final expression is 1/x⁹⁵/⁷.