Simplify x^(-2/3) and Find Square Root

Published on February 28, 2026

Algebra

Solve for x given x = (27/125)^(-2/3) and then calculate the value of sqrt(x) using exponent rules.

Question

Answer

Here is the step-by-step solution to the problem.

The problem asks to find the value of

given that:

Step 1: Simplify the expression for .

We use the property of exponents that

and

Next, we express the numerator and the denominator as powers with an exponent of 3, since the denominator of the exponent is 3:

So,

Substitute this back into the expression for

Using the property of exponents

Step 2: Calculate .

We need to find

Since

, and

is positive:

Alternative Method (Calculating directly):

We know that

Using the property

Apply the negative exponent rule

The exponent

means taking the cube root:

Since

and

Conclusion:
The value of

, which corresponds to option (a).

The final answer is:

Theorems

• Negative Exponent Rule (Reciprocal)

For any non-zero number

and any real number

. For fractions,

• Power of a Power Rule

For any real number

and any real numbers

and

• Fractional Exponent Rule (Cube Root)

For any real number

• Power of a Quotient Rule

For any real numbers

and

(with

) and any real number

• Square Root of a Square

For any real number

. Since the result

is positive,

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Simplify x^(-2/3) and Find Square Root

Question

Answer

Theorems

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