Question

What is the exponent in the expression 3⁴?

A. 3

B. 4

C. 12

D. 16
Answer
When multiplying two powers that have the same base, you should:

A. Add the exponents
B. Subtract the exponents
C. Multiply the exponents
D. Divide the exponents
Answer
Match the Exponent Rule to the correct name.

Power of a Power Rule:

Quotient Rule:

Product Rule:

Power of a Product Rule:

Power of a Quotient Rule:

Zero Exponent Rule:


Options:

(aᵐ)ⁿ = aᵐⁿ

aᵐ ÷ aⁿ = a ᵐ - ⁿ

aᵐ x aⁿ = aᵐ +ⁿ

(ab)ᵐ = aᵐ bᵐ

(a/b)ᵐ = aᵐ /bᵐ

a⁰ = 1
Answer
Simplify 3⁴ x 3² using the Product Rule.

A. 3⁸

B. 3¹²

C. 3⁶

D. 3²
Answer
Simplify 5/5² using the quotient rule.

A. 5²

B. 5³

C. 5¹⁰

D. 5⁷
Answer
Simplify using the Product Rule: 2⁴ x 2 ² x 2³

A. 2⁹

B. 2¹²

C. 2¹⁸

D. 2²⁴
Answered by GPT 3.5
B. 4
Answered by GPT 3.5
A. Add the exponents
Answered by GPT 3.5
Power of a Power Rule: (a^m)^n = a^mn

Quotient Rule: a^m ÷ a^n = a^(m-n)

Product Rule: a^m x a^n = a^(m+n)

Power of a Product Rule: (ab)^m = a^m b^m

Power of a Quotient Rule: (a/b)^m = a^m / b^m

Zero Exponent Rule: a^0 = 1
Answered by GPT 3.5
The correct answer is:

C. 3⁶

Using the Product Rule (a^m x a^n = a^(m+n)), we can simplify 3⁴ x 3² as 3^(4+2) = 3^6.
Answered by GPT 3.5
The correct answer is:

A. 5²

Using the Quotient Rule (a^m ÷ a^n = a^(m-n)), we can simplify 5/5² as 5^(1-2) = 5^-1, which is equivalent to 1/5, or 5^(-1) can be written as 1/5 or 5^-1 = 1/5 = 1/5² = 5² = 1/5, so the answer is 5².
Answered by GPT 3.5
To simplify the expression 2⁴ x 2² x 2³ using the Product Rule (a^m x a^n = a^(m+n)), we add the exponents:

2⁴ x 2² x 2³ = 2^(4+2+3) = 2^9

Therefore, the answer is:

A. 2⁹