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

Question

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

Answer 1

The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\).

Let's analyze each option:

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

B) \((7^4)^8\): This uses the Power Rule because it is in the form \((a^m)^n\), which can be simplified to \(7^{4 \cdot 8} = 7^{32}\).

C) \((7^8) \times (7^{10})\): This involves the Product of Powers Rule, which states that \(a^m \times a^n = a^{m+n}\). It does not specifically use the Power Rule of Exponents.

D) \(12^9\): 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

Answer 2

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

Answer 3

To simplify \(4^{10}\) using the Power Rule of Exponents, we need an equivalent expression that can be represented in the form \((a^m)^n\).

Let’s analyze each option to see which one correctly expands to \(4^{10}\):

A) \((4^{12})^2\): Using the Power Rule, this simplifies to \(4^{12 \cdot 2} = 4^{24}\), which is not equivalent to \(4^{10}\).

B) \((4^2)^8\): Using the Power Rule, this simplifies to \(4^{2 \cdot 8} = 4^{16}\), which is not equivalent to \(4^{10}\).

C) \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\): This is equal to \(4^7\), which is not equivalent to \(4^{10}\).

D) \((4^5)^2\): Using the Power Rule, this simplifies to \(4^{5 \cdot 2} = 4^{10}\), which is equivalent to \(4^{10}\).

The correct choice that simplifies to \(4^{10}\) is:

D) (4^5)^2