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Chapter 2: Problem 40

Simplify. \(\left(\frac{10 b^{3} c^{5}}{15 a}\right)^{2}\)

Short Answer

Expert verified
\(\frac{4 b^6 c^{10}}{9 a^2}\)

Step by step solution

01

Distribute the Power to All Elements Inside the Parentheses

To simplify the given expression, we'll first distribute the square (power of 2) to the numerator, denominator, and all individual terms inside the parentheses: \[\left(\frac{10 b^{3} c^{5}}{15 a}\right)^{2} = \frac{(10^2)(b^3)^2 (c^5)^2}{(15^2)(a^2)}\]
02

Calculate the Exponents

Now, we calculate the exponent for each term: \[\frac{(10^2)(b^3)^2 (c^5)^2}{(15^2)(a^2)} = \frac{100 b^6 c^{10}}{225 a^2}\]
03

Simplify the Numerical Fraction

Following this, we simplify the numerical fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD): \[\frac{100}{225} = \frac{100 \div 25}{225 \div 25} = \frac{4}{9}\]
04

State the Simplified Expression

Finally, we put the simplified numerical fraction together with the algebraic terms, resulting in the fully simplified expression: \[\frac{4 b^6 c^{10}}{9 a^2}\]

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Most popular questions from this chapter

Write each number in scientific notation. The diameter of an atom is about \(0.00000001 \mathrm{cm}\)

Express each number in scientific notation, then solve the problem. In Wisconsin in 2001 , approximately \(1,300,000\) cows produced \(2.21 \times 10^{10}\) lb of milk. On average, how much milk did each cow produce?

Simplify using the quotient rule. $$\frac{6 v^{1} w}{54 v^{2} w^{-5}}$$

Perform the operation as indicated. Write the final answer without an exponent. \(\left(2.3 \times 10^{3}\right)\left(3 \times 10^{2}\right)\)

Perform the operation as indicated. Write the final answer without an exponent. \(\frac{8.4 \times 10^{12}}{-7 \times 10^{9}}\)
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