Q14. Simplify the expression. Show th... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q14. (page 665)

Simplify the expression. Show the work
${(\frac{鈭� 2 r^{鈭� 2} q^{5} t^{2}}{5 r^{4} q^{2} t^{鈭� 3}})}^{鈭� 2}$

Short Answer

Expert verified

The simplified version of ${(\frac{鈭� 2 r^{鈭� 2} q^{5} t^{2}}{5 r^{4} q^{2} t^{鈭� 3}})}^{鈭� 2}$ is role="math" $\frac{25 r^{12}}{4 q^{6} t^{10}}$ .

Step by step solution

Step 1. State the division rule of ‘laws of indices’.

If a fraction is raised to a power, then every terms of the fraction is raised to the power.

In general: ${(\frac{x}{y})}^{m} = \frac{x^{m}}{y^{m}}$

Step 2. State the division rule of ‘laws of indices’.

If the two terms having the same base are divided, then the base is written only once and the indices are subtracted.

In general: $\frac{x^{m}}{x^{n}} = x^{m 鈭� n}$

Step 3. State the ‘Law of indices’ for power of index numbers.

If a term with a power is itself raised to a power, then the powers are multiplied together.

In general: ${(x^{m})}^{n} = x^{m 脳 n}$

Step 4. State the law of indices for negative index.

If a term has negative index, then the reciprocal of that term is taken and raise it with the positive index.

In general: $x^{鈭� n} = \frac{1}{x^{n}}$

Step 4. Simplify the expression.

Using laws of indices simplify ${(\frac{鈭� 2 r^{鈭� 2} q^{5} t^{2}}{5 r^{4} q^{2} t^{鈭� 3}})}^{鈭� 2}$

$\begin{array}{l} {(\frac{鈭� 2 r^{鈭� 2} q^{5} t^{2}}{5 r^{4} q^{2} t^{鈭� 3}})}^{鈭� 2} = {[(\frac{鈭� 2}{5}) (\frac{r {}^{鈭� 2}}{r^{4}}) (\frac{q^{5}}{q^{2}}) (\frac{t^{2}}{t^{鈭� 3}})]}^{鈭� 2} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [颁辞濒濒别肠迟鈥夆赌塼丑别鈥夆赌塴颈办别鈥夆赌塼别谤尘蝉鈥夆赌塼辞驳别迟丑别谤] \\ = {[(\frac{鈭� 2}{5}) (r^{鈭� 2 鈭� 4}) (q^{5 鈭� 2}) (t^{2 鈭� (鈭� 3)})]}^{鈭� 2} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [Using \frac{x^{m}}{x^{n}} = x^{m 鈭� n}] 鈥夆赌夆赌夆赌夆赌夆赌� \\ = {[(\frac{鈭� 2}{5}) (r^{鈭� 6}) (q^{3}) (t^{2 + 3})]}^{鈭� 2} \\ = {[(\frac{鈭� 2}{5}) (r^{鈭� 6}) (q^{3}) (t^{5})]}^{鈭� 2} \\ = {(\frac{鈭� 2}{5})}^{鈭� 2} {(r^{鈭� 6})}^{鈭� 2} {(q^{3})}^{鈭� 2} {(t^{5})}^{鈭� 2} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [鲍蝉颈苍驳鈥夆赌� {(x y)}^{m} = x^{m} y^{m}] \\ = {(\frac{鈭� 2}{5})}^{鈭� 2} (r^{(鈭� 6) (鈭� 2)}) (q^{(3) (鈭� 2)}) (t^{(5) (鈭� 2)}) 鈥夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌� [鲍蝉颈苍驳鈥夆赌� {(x^{m})}^{n} = x^{m 脳 n}] \\ = {(\frac{鈭� 2}{5})}^{鈭� 2} (r^{12}) (q^{鈭� 6}) (t^{鈭� 10}) \\ = {(\frac{5}{鈭� 2})}^{2} (r^{12}) (\frac{1}{q^{6}}) (\frac{1}{t^{10}}) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆€夆€� [鲍蝉颈苍驳鈥夆赌� x^{鈭� n} = \frac{1}{x^{n}}] \\ = \frac{{(5)}^{2}}{{(鈭� 2)}^{2}} 脳 \frac{r^{12}}{q^{6} t^{10}} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [鲍蝉颈苍驳鈥夆赌� {(\frac{x}{y})}^{m} = \frac{x^{m}}{y^{m}}] \\ = \frac{25}{4} 脳 \frac{r^{12}}{q^{6} t^{10}} 鈥夆赌夆赌夆赌夆赌� \\ = \frac{25 r^{12}}{4 q^{6} t^{10}} 鈥夆赌夆赌夆赌� \end{array}$

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91影视

Simplify the expression. Show the work
${(\frac{鈭� 2 r^{鈭� 2} q^{5} t^{2}}{5 r^{4} q^{2} t^{鈭� 3}})}^{鈭� 2}$

Short Answer

Step by step solution

Step 1. State the division rule of ‘laws of indices’.

Step 2. State the division rule of ‘laws of indices’.

Step 3. State the ‘Law of indices’ for power of index numbers.

Step 4. State the law of indices for negative index.

Step 4. Simplify the expression.

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91影视

Simplify the expression. Show the work(鈭�2r鈭�2q5t25r4q2t鈭�3)鈭�2

Short Answer

Step by step solution

Step 1. State the division rule of ‘laws of indices’.

Step 2. State the division rule of ‘laws of indices’.

Step 3. State the ‘Law of indices’ for power of index numbers.

Step 4. State the law of indices for negative index.

Step 4. Simplify the expression.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify the expression. Show the work
${(\frac{鈭� 2 r^{鈭� 2} q^{5} t^{2}}{5 r^{4} q^{2} t^{鈭� 3}})}^{鈭� 2}$