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, ${(a^{m})}^{n} = a^{m \cdot n}$

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

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

$2^{3 \cdot 2} r^{9 \cdot 2} t^{3 \cdot 2}$

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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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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Simplify each expression.2r3t32

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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