Final answer:
To simplify the expression a⁻³ and use only positive exponents, we convert it to 1/a³, as a negative exponent indicates that the base should be inverted and the exponent considered as positive.
Step-by-step explanation:
To simplify each of the following expressions by using positive exponents only, we need to apply the rules of exponents. Specifically, for the expression a⁻³, we need to convert the negative exponent to a positive one. This can be achieved by taking the reciprocal of the base and then raising it to the power indicated by the absolute value of the exponent.
Therefore, a⁻³ can be simplified to 1/a³. This is because a negative exponent indicates that the base should be on the opposite side of the fraction line. So in essence, the negative sign in the exponent inverts the base from the numerator to the denominator and the exponent becomes positive.
Another way to think about this is using the law of exponents where a⁻³ = 1/a³. This law helps us to simplify expressions and keep the exponents positive, which is often easier to interpret and work with.