Write each expression with a single rational exponent. Show each step of your process. Which expressions are equivalent? Justify your reasoning.

Question

Write each expression with a single rational exponent. Show each step of your process. Which expressions are equivalent? Justify your reasoning.

1. 
2. 
3. 
4. 

Answer 1

1) x^.75

2) x^1 = x

3) x^1.1

4) x^1 = x

.75, 1 and 1.1 are rational exponents

treat the exponent inside the radical as the numerator and the number outside to the left of the radical sign as the denominator for 1) and 3)

what's inside the radical for 3) is x^5(x^4)(x^2) = x^(5+5+2) = x^11. x^(11/10) = x^1.1

for 2) flip the fraction upside, down, switch numerator and denominator, then change the sign of the exponent

1/x^-1 = x^-1/1 = x^-1, change the sign to get x^1 = x with an implicit 1 as the exponent

or 1/x^-1 = 1/(1/x) = 1(x/1) = x flip the divisor upside down and change division to multiplication

for 4) x^1/3(x^1/3)(x^1/3) add the exponents: x^(1/3+1/3+1/3) = x^(3/3) = x^1 =x

expressions 2) and 4) are equivalent