Understanding the Power Rule of Exponents

The video tutorial explains how to simplify expressions with exponents using the power rule. It begins with an introduction to the concept and then explains the power rule, which states that raising a power to another power involves multiplying the exponents. The tutorial provides a detailed example using x squared raised to the third power, demonstrating how to multiply the exponents and simplify the expression. Finally, the power rule is applied to a more complex expression, showing how to simplify it step by step.

What is the initial expression that needs to be simplified using the power rule?

• x to the third power raised to the fourth power times x squared raised to the fifth power

• x squared raised to the third power times x to the fourth power

• x to the fifth power raised to the second power times x to the third power

• x to the fourth power raised to the third power times x squared

What does the power rule of exponents state?

• Add the exponents when multiplying powers with the same base

• Divide the exponents when raising a power to another power

• Subtract the exponents when dividing powers with the same base

• Multiply the exponents when raising a power to another power

In the example x squared raised to the third power, what is the resulting exponent?

• x to the fifth power

• x to the sixth power

• x to the fourth power

• x to the seventh power

How many times is x multiplied by itself in the expression x squared raised to the third power?

• Three times

• Six times

• Five times

• Four times

What is the result of multiplying x squared by itself three times?

• x to the sixth power

• x to the fourth power

• x to the seventh power

• x to the fifth power

Why can exponents be added when multiplying powers with the same base?

• Because the powers are being divided

• Because the bases are different

• Because it represents repeated multiplication of the base

• Because it represents repeated addition of the base

What is the simplified form of x to the third power raised to the fourth power?

• x to the eighth power

• x to the tenth power

• x to the twelfth power

• x to the seventh power

What is the simplified form of x squared raised to the fifth power?

• x to the eleventh power

• x to the ninth power

• x to the eighth power

• x to the tenth power

What is the final simplified expression of the original problem?

• x to the twentieth power

• x to the twenty-second power

• x to the twenty-fourth power

• x to the eighteenth power

What is the result of x to the 12th power times x to the 10th power?

• x to the 18th power

• x to the 20th power

• x to the 24th power

• x to the 22nd power