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Chapter 0: Problem 100

Simplify using properties of exponents. $$\frac{\left(2 y^{\frac{1}{5}}\right)^{4}}{y^{\frac{3}{10}}}$$

Short Answer

Expert verified
The simplified version of the given expression is \(16y^{\frac{1}{2}}\).

Step by step solution

01

Simplify Inner Exponent

Start by simplifying the inner exponent where \(2y^{\frac{1}{5}}\) is raised to power of 4. The expression turns into \(2^4 * (y^{\frac{1}{5}})^4\) which simplifies to \(16 * y^{\frac{4}{5}}\) as when raising an exponent to another exponent, the exponents are multiplied.
02

Divide the Exponents

To divide exponents with the same base, the rule is to subtract the exponent in the denominator from the exponent in the numerator. So the expression \( \frac{16y^{\frac{4}{5}}}{y^{\frac{3}{10}}}\) turns into \(16 * y^{(\frac{4}{5})-(\frac{3}{10})}\) .
03

Subtract the Exponents

Subtracting the exponents, maintaining a common denominator to make calculations easy, yields \(16y^{(\frac{8}{10} - \frac{3}{10})}\). This simplifies to \(16y^{\frac{1}{2}}\).

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Most popular questions from this chapter

Perform the indicated operations. $$ [(7 x+5)+4 y][(7 x+5)-4 y] $$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$2 x^{4}\left(8 x^{4}+3 x\right)$$

How do you know if a number is written in scientific notation?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$7^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}=49$$
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