Which is equivalent tostartroot 10 endroot superscript three-fourths x

General
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which is equivalent tostartroot 10 endroot superscript three-fourths x

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Which is equivalent to \sqrt[4]{10^3} \times x?

To determine the equivalent form of the given expression \sqrt[4]{10^3} \times x, you need to understand the expression and simplify it step by step. The given expression can be interpreted in two parts: \sqrt[4]{10^3} and \times x.

Let’s break it down:

  1. Expressing the Radix and Exponent:

    The given term \sqrt[4]{10^3} can be understood as 10^{\frac{3}{4}}. This is due to the property of exponents that states \sqrt[n]{a^m} = a^{\frac{m}{n}}.

  2. Simplifying the Given Expression:

    a. Start with the given expression:

    \sqrt[4]{10^3} \times x

    b. Using the exponent rule:

    10^{\frac{3}{4}} \times x

    Therefore, \sqrt[4]{10^3} \times x is equivalent to 10^{\frac{3}{4}} \times x.

  3. Alternative Representation:

    The expression 10^{\frac{3}{4}} \times x doesn’t require further simplification, but it can be represented in another way as:

    (10^{3})^{\frac{1}{4}} \times x

    This also simplifies back to 10^{\frac{3}{4}} confirming consistency in the calculation.

Conclusion:

To summarize, the expression \sqrt[4]{10^3} \times x is equivalent to 10^{\frac{3}{4}} \times x. This form is easier to comprehend, and it shows the relationship between the base 10 and the fractional exponent \frac{3}{4}.

If you have any further questions or need additional explanations, feel free to ask!