Power and Exponent Rules

This lesson on exponents covers the concept of raising a power to another power, using examples with both numbers and variables. It explains the general rule of multiplying exponents when raising a power to a power and addresses common mistakes in simplifying expressions. The lesson concludes with a challenge problem that applies all the exponent laws discussed.

What topics were covered in the previous lessons on exponents?

• Exponentiation and roots

• Logarithms and exponents

• Multiplication and division of exponents

• Addition and subtraction of exponents

What is the result of raising 2 to the power of 3, then raising that result to the power of 4?

• 2^36

• 2^7

• 2^12

• 2^24

When raising a power to another power, what operation is performed on the exponents?

• Addition

• Division

• Multiplication

• Subtraction

How can the expression (a^2 * b^4)^3 be simplified using the power-to-power rule?

• a^5 * b^10

• a^8 * b^7

• a^4 * b^8

• a^6 * b^12

What is the general rule for raising a power to a power?

• a^m / a^n = a^(m-n)

• a^m * a^n = a^(m+n)

• a^m + a^n = a^(m+n)

• (a^m)^n = a^(m*n)

How do you simplify (x^5 / y^4)^4 using the power-to-power rule?

• x^9 / y^8

• x^20 / y^16

• x^10 / y^12

• x^15 / y^20

What is the result of raising (a*b)^2?

• a^4 * b^4

• a^3 * b^3

• a^5 * b^5

• a^2 * b^2

How does the expression (a + b)^2 differ from (a*b)^2?

• Both involve only addition

• They are the same

• (a + b)^2 involves addition, (a*b)^2 involves multiplication

• (a + b)^2 involves multiplication, (a*b)^2 involves addition

What is the simplified form of (a*b)^-2?

• a^2 * b^2

• 1/(a^2 * b^2)

• a*b

• 1/(a*b)

How do you simplify (a + b)^-2?

• a + b

• 1/(a + b)

• a^2 + 2ab + b^2

• 1/(a^2 + 2ab + b^2)