Question

Given the algebraic expression the quantity 64 times x to the two-thirds power end quantity to the negative one-third power comma, create an equivalent expression.
1 divided by the quantity 4 times x to the one-third power end quantity
1 divided by the quantity 4 times x to the two-ninths power end quantity
4 times x to the one-third power
4 times x to the two-ninths power

Answer 1

The given algebraic expression is equal to 1 divided by the quantity 4 times x to the two-ninths power end quantity. The correct option is B.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given algebraic expression can be simplified using the exponential properties. Therefore, the simplification of the algebraic expression can be done as shown below.

$(64x^{\frac23})^{-\frac13}$

$= (4^3)^{-\frac13} \times x^{(\frac23 \times -\frac13)}\\\\= 4^{(3 \times -\frac13)} \times x^{(\frac23 \times -\frac13)}\\\\= 4^{-1} \times x^{-\frac29}\\\\=\dfrac{1}{4x^{\frac29}}$

Hence, the correct option is B.

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