Question
Write 3(a/b^-2)^-3 in its simplest form
A. 3/a^2•b^5
B. 3a^3/b^6
C. 3/ab^6
D. 3/a^3•b^6
A. 3/a^2•b^5
B. 3a^3/b^6
C. 3/ab^6
D. 3/a^3•b^6
Answers
GPT 3.5
To simplify 3(a/b^-2)^-3, we need to apply the power rule for exponents and distribute the exponent outside of the parentheses.
First, we'll distribute the exponent of -3 to both a and b^-2.
[(a^-3)/(b^(-2)(-3))]
Next, we'll simplify the exponents by applying the negative exponent rule and multiplying the exponents.
[(a^-3)/(b^6)]
Finally, we can rewrite this expression in its simplest form by moving the negative exponents to the numerator and simplifying any negative exponents.
[b^6/a^3]
Therefore, the answer is D. 3/a^3•b^6.
First, we'll distribute the exponent of -3 to both a and b^-2.
[(a^-3)/(b^(-2)(-3))]
Next, we'll simplify the exponents by applying the negative exponent rule and multiplying the exponents.
[(a^-3)/(b^6)]
Finally, we can rewrite this expression in its simplest form by moving the negative exponents to the numerator and simplifying any negative exponents.
[b^6/a^3]
Therefore, the answer is D. 3/a^3•b^6.