Chapter 6: Q. 145 (page 711)

In the following exercises, simplify each expression.
${(x^{2})}^{4} \cdot (x)$ ³2

Short Answer

Expert verified

The simplified form of the given expression is $x^{14}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression.

${(x^{2})}^{4} \cdot {(x^{3})}^{2}$

Step 2. Use the Product to a Power Property.

${(x^{2})}^{4} \cdot {(x^{3})}^{2} = (x^{2 \cdot 4}) \cdot (x^{3 \cdot 2}) {(x^{2})}^{4} \cdot {(x^{3})}^{2} = x^{8} \cdot x^{6}$

Multiply the constants and add the exponents.
${(x^{2})}^{4} \cdot {(x^{3})}^{2} = x^{8 + 6} {(x^{2})}^{4} \cdot {(x^{3})}^{2} = x^{14}$

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In the following exercises, simplify each expression.
${(x^{2})}^{4} \cdot (x)$ ³2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use the Product to a Power Property.

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Step by step solution

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In the following exercises, simplify each expression.
${(x^{2})}^{4} \cdot (x)$ ³2