Answer :
the correct answer is:
B. [tex]\(\frac{1}{4x^{2/9}}\)[/tex]
To create an equivalent expression for [tex]\((64x^{2/3})^{-1/3}\)[/tex], we'll use exponent rules.
Apply the negative exponent rule, which states that [tex]\(a^{-n} = \frac{1}{a^n}\):[/tex]
[tex]\[(64x^{2/3})^{-1/3} = \frac{1}{(64x^{2/3})^{1/3}}\][/tex]
Apply the power of a power rule, which states that [tex]\((a^m)^n = a^{mn}\):[/tex]
[tex]\[\frac{1}{(64x^{2/3})^{1/3}} = \frac{1}{64^{1/3} (x^{2/3})^{1/3}}\][/tex]
Simplify the expression inside the parentheses:
[tex]\[64^{1/3} = (4^3)^{1/3} = 4\][/tex]
[tex]\[(x^{2/3})^{1/3} = x^{\frac{2}{3} \cdot \frac{1}{3}} = x^{2/9}\][/tex]
Substitute the simplified expressions back into the equation:
[tex]\[\frac{1}{64^{1/3} (x^{2/3})^{1/3}} = \frac{1}{4 \cdot x^{2/9}}\][/tex]
So, the equivalent expression is [tex]\(\frac{1}{4x^{2/9}}\)[/tex], which matches option B. Therefore, the correct answer is:
B. [tex]\(\frac{1}{4x^{2/9}}\)[/tex]
The complete question is:
Given the algebraic expression[tex](64x^2/3)^-1/3[/tex] create an equivalent expression.
A. 1/4x^1/3
B. 1/4x^2/9
C. 4x^1/3
D. 4x^2/9
