Q15. Simplify each expression.2r3t32... [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 7: Q15. (page 460)

Simplify each expression.
${[{(2 r^{3} t)}^{3}]}^{2}$

Short Answer

Expert verified

The expression ${[{(2 r^{3} t)}^{3}]}^{2}$ can be simplified as $64 r^{18} t^{6}$ .

Step by step solution

Step 1. Write property of power of a product.

For any real number x, y and any integer n, ${(x y)}^{n} = x^{n} y^{n}$ .

Step 2. Apply the property of power of a product.

Apply the property of power of a product to the given expression.

${(2^{3})}^{2} {[{(r^{3})}^{3}]}^{2} {(t^{3})}^{2}$

Step 3. Write the property of power of a power.

For any real number a and any integers m and n, ${(a^{m})}^{n} = a^{m 鈰� n}$

Step 4. Apply the property of power of a power.

Apply the property of power of a power to the expression in step 2.

$2^{3 鈰� 2} r^{9 鈰� 2} t^{3 鈰� 2}$

Step 5. Simplify the obtained expression.

Simplify the expression in step.

$64 r^{18} t^{6}$

Therefore, ${[{(2 r^{3} t)}^{3}]}^{2}$ can be simplified to $64 r^{18} t^{6}$ .

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91影视

Simplify each expression.
${[{(2 r^{3} t)}^{3}]}^{2}$

Short Answer

Step by step solution

Step 1. Write property of power of a product.

Step 2. Apply the property of power of a product.

Step 3. Write the property of power of a power.

Step 4. Apply the property of power of a power.

Step 5. Simplify the obtained expression.

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