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Y_Kistochka [10]
3 years ago
5

Describe how to transform the quantity of the fifth root of x to the seventh power, to the third powerinto an expression with a

rational exponent. Make sure you respond with complete sentences.
Mathematics
1 answer:
geniusboy [140]3 years ago
7 0
(\sqrt[5]{x^{7}})^{3}=(x^{\frac{7}{5}})^{3}=x^{\frac{7\cdot3}{5}}=x^{\frac{21}{5}}

The root is equivalent to a fractional power with that number as the denominator. Otherwise, the rules of exponents apply.
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We can simply observe that.

  1. 0.777... is rational, because it is a number with infinite but repeating decimal part.
  2. 1/3 is rational, because it's the division between two integers
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Since the product of two rational numbers is always rational, we have that

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