Which expression is correctly developed to use the Power Rule of Exponents?

A) (-5)^0
B)(7^4)^8
C) (7^8) x (7^10)
D) 12^9

3 answers

The Power Rule of Exponents states that (am)n=amn.

Let's analyze each option:

A) (5)0: This evaluates to 1 but does not use the Power Rule.

B) (74)8: This uses the Power Rule because it is in the form (am)n, which can be simplified to 748=732.

C) (78)×(710): This involves the Product of Powers Rule, which states that am×an=am+n. It does not specifically use the Power Rule of Exponents.

D) 129: This is a single base raised to an exponent, so does not invoke the Power Rule.

Based on the analysis, the correct expression that uses the Power Rule of Exponents is:

B) (7^4)^8

If the expression 4^10 was simplified using the power rule of exponents, what is an equivalent expanded expression?
A)(4^12)^2
B) (4^2)^8
C)4 x 4 x 4 x 4 x 4 x 4 x 4
D) (4^5)^2

To simplify 410 using the Power Rule of Exponents, we need an equivalent expression that can be represented in the form (am)n.

Let’s analyze each option to see which one correctly expands to 410:

A) (412)2: Using the Power Rule, this simplifies to 4122=424, which is not equivalent to 410.

B) (42)8: Using the Power Rule, this simplifies to 428=416, which is not equivalent to 410.

C) 4×4×4×4×4×4×4: This is equal to 47, which is not equivalent to 410.

D) (45)2: Using the Power Rule, this simplifies to 452=410, which is equivalent to 410.

The correct choice that simplifies to 410 is:

D) (4^5)^2

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