(16/49)^-1/2

Jasonbradley

2 min read

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Jun 16, 2024

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Understanding (16/49)^(-1/2)

This expression represents a fractional exponent applied to a fraction. Let's break down the steps involved in solving it:

1. Fractional Exponents

Fractional exponents represent roots. The denominator of the fraction indicates the type of root, while the numerator indicates the power to which the base is raised.

• Example: x^(1/2) represents the square root of x. x^(1/3) represents the cube root of x.

2. Applying the Exponent

In our case, we have (16/49)^(-1/2). Let's analyze the parts:

• -1/2: This exponent indicates the square root (denominator is 2) and also the reciprocal (negative sign).

Applying the exponent step-by-step:

1. Reciprocal: (16/49)^(-1/2) = (49/16)^(1/2)
2. Square Root: (49/16)^(1/2) = √(49/16)
3. Simplify: √(49/16) = 7/4

Final Result

Therefore, (16/49)^(-1/2) simplifies to 7/4.

Key Points

• Fractional exponents represent roots.
• The negative sign in the exponent indicates the reciprocal.
• Remember the properties of square roots and fractions to simplify the expression.