which of the following is equivalent to (a1/2 times b1/3)^1/2?
a. a times b 5/6
b. a 1/2 times b 2/5
c. a times b 1/5
d. a 1/4 times b 1/6
3 answers
b. a 1/2 times b 2/5
why
To simplify the expression (a^(1/2) * b^(1/3))^(1/2), we can use the properties of exponents. When raising an exponent to another exponent, we need to multiply the exponents.
Therefore, (a^(1/2) * b^(1/3))^(1/2) = a^(1/2 * 1/2) * b^(1/3 * 1/2) = a^(1/4) * b^(1/6)
This simplifies to a^(1/4) * b^(1/6), which corresponds to option b.
Therefore, (a^(1/2) * b^(1/3))^(1/2) = a^(1/2 * 1/2) * b^(1/3 * 1/2) = a^(1/4) * b^(1/6)
This simplifies to a^(1/4) * b^(1/6), which corresponds to option b.