index laws

Question 1

What is the rule for the product of powers with the same base?

Answer 1

Add the exponents: a^m * a^n = a^(m+n)

This rule is used for simplifying expressions involving powers with the same base.

Question 2

What is the rule for the quotient of powers with the same base?

Answer 2

Subtract the exponents: a^m / a^n = a^(m-n)

This rule applies when dividing terms with the same base.

Question 3

What does it mean to raise a power to another power?

Answer 3

Multiply the exponents: (a^m)^n = a^(m*n)

This rule indicates how to handle exponentiation involving powers.

Question 4

What is the power of a product rule?

Answer 4

Raise each factor to the power: (ab)^n = a^n * b^n

This rule applies when raising a product to a power.

Question 5

What is the power of a quotient rule?

Answer 5

Raise both the numerator and denominator to the power: (a/b)^n = a^n / b^n

This rule is used when raising a quotient to a power.

Question 6

What is the value of any non-zero number raised to the power of zero?

Answer 6

1: a^0 = 1

This is a fundamental property of exponents.

Question 7

What does a negative exponent indicate?

Answer 7

The reciprocal of the base raised to the positive value of the exponent: a^-n = 1/a^n

This rule is important for understanding negative exponents.

Question 8

Calculate 2^3 * 2^2.

Answer 8

2^(3+2) = 2^5 = 32

This example illustrates the product of powers rule.

Question 9

Calculate 5^4 ÷ 5^2.

Answer 9

5^(4-2) = 5^2 = 25

This example illustrates the quotient of powers rule.

Question 10

What is (3^2)^3 equal to?

Answer 10

3^(2*3) = 3^6 = 729

This example illustrates raising a power to a power.

Question 11

What is (2x)^3 equal to?

Answer 11

2^3 * x^3 = 8x^3

This example illustrates the power of a product rule.

Question 12

What is the value of 4^0?

Answer 12

1

This demonstrates the rule for zero exponents.

Question 13

Calculate 2^-2.

Answer 13

1/2^2 = 1/4

This example illustrates the negative exponent rule.