Question
show all the steps it took to get your answer.
write the expression in simplest form.
(8a^3)^-4/3
write the expression in simplest form.
(8a^3)^-4/3
Answers
GPT 3.5
To simplify (8a^3)^(-4/3), first convert the negative exponent to a positive one by moving the base to the denominator:
1/ (8a^3)^(4/3)
Next, apply the power rule for exponents by raising both the base and the exponent to the power of 4/3:
1/ (2^4 * (a^3) ^ 4/3)
Simplify the expression inside the parentheses:
1/ (16 * a^(3 * 4/3))
1/ (16 * a^4)
Finally, simplify the expression further by multiplying 16 and a^4:
1/16a^4
Therefore, the expression (8a^3)^(-4/3) in simplest form is 1/16a^4.
1/ (8a^3)^(4/3)
Next, apply the power rule for exponents by raising both the base and the exponent to the power of 4/3:
1/ (2^4 * (a^3) ^ 4/3)
Simplify the expression inside the parentheses:
1/ (16 * a^(3 * 4/3))
1/ (16 * a^4)
Finally, simplify the expression further by multiplying 16 and a^4:
1/16a^4
Therefore, the expression (8a^3)^(-4/3) in simplest form is 1/16a^4.