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Chapter 0: Problem 97

Simplify using properties of exponents. $$\left(25 x^{4} y^{6}\right)^{\frac{1}{2}}$$

Short Answer

Expert verified
The simplified expression is \(5x^{2}y^{3}\).

Step by step solution

01

Identify the expression

The expression given is \( \left(25 x^{4} y^{6}\right)^{\frac{1}{2}} \). This can be separated into three separate terms -- \(25^{\frac{1}{2}}\), \(x^{4*\frac{1}{2}}\), and \(y^{6*\frac{1}{2}}\).
02

Apply properties of exponents

Now, apply the properties of exponents to each term. \(25^{\frac{1}{2}}\) is the square root of 25, which gives 5. Also, multiply the exponents in \(x^{4*\frac{1}{2}}\) and \(y^{6*\frac{1}{2}}\), which gives \(x^{2}\) and \(y^{3}\) respectively.
03

Combine terms

Putting these terms together will yield the final simplified expression, which is \(5x^{2}y^{3}\).

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

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

The early Greeks believed that the most pleasing of all rectangles were golden rectangles, whose ratio of width to height is $$\frac{w}{h}=\frac{2}{\sqrt{5}-1}$$ The Parthenon at Athens fits into a golden rectangle once the triangular pediment is reconstructed. (IMAGE CANT COPY) Rationalize the denominator of the golden ratio. Then use a calculator and find the ratio of width to height, correct to the nearest hundredth, in golden rectangles.

There are approximately \(3.2 \times 10^{7}\) seconds in a year. According to the United States Department of Agriculture, Americans consume 127 chickens per second. How many chickens are eaten per year in the United States? Express the answer in scientific notation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$
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