Chapter 7: Q17. (page 460)

Simplify each expression.
${(2 x^{2})}^{3} {(x^{3})}^{3}$

Short Answer

Expert verified

The expression ${(2 x^{2})}^{3} {(x^{3})}^{3}$ can be simplified as $8 x^{15}$ .

Step by step solution

Step 1. 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 2. Apply the property of power of a power.

Apply the property of power of a power to the expression in step 1.

$2^{1 \cdot 3} x^{2 \cdot 3} x^{3 \cdot 3} = 2^{3} x^{6} x^{9}$

Step 3. Write the property of product of powers.

For any real number a and any integers m and n, $a^{m} \cdot a^{n} = a^{m + n}$ .

Step 4. Apply property of product of powers.

Apply the property of product of powers to the expression obtained in step 2.

$8 x^{6 + 9} = 8 x^{15}$

Therefore, ${(2 x^{2})}^{3} {(x^{3})}^{3}$ can be simplified as $8 x^{15}$ .

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Simplify each expression.
${(2 x^{2})}^{3} {(x^{3})}^{3}$

Short Answer

Step by step solution

Step 1. Write the property of power of a power.

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

Step 3. Write the property of product of powers.

Step 4. Apply property of product of powers.

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Simplify each expression.2x23x33

Short Answer

Step by step solution

Step 1. Write the property of power of a power.

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

Step 3. Write the property of product of powers.

Step 4. Apply property of product of powers.

One App. One Place for Learning.

Most popular questions from this chapter

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Simplify each expression.
${(2 x^{2})}^{3} {(x^{3})}^{3}$