which expression is correctly developed to use the power rule of exponents?

12^9
(-5)^0
(7^8) . (7^10)
(7^4)^8

5 answers

To correctly develop expressions using the power rule of exponents, we can apply the following rules:

  1. The power of a product rule: \((a^m)(a^n) = a^{m+n}\)
  2. The power of a power rule: \((a^m)^n = a^{m \cdot n}\)
  3. The zero exponent rule: \(a^0 = 1\) (for any \(a \neq 0\))

Let's look at each expression:

  1. \(12^9\): This expression is already simplified and doesn't indicate further simplification using the power rules.

  2. \((-5)^0\): By the zero exponent rule, this simplifies to 1.

  3. \((7^8) \cdot (7^{10})\): Using the power of a product rule, this simplifies to:
    \((7^8) \cdot (7^{10}) = 7^{8+10} = 7^{18}\).

  4. \((7^4)^8\): By the power of a power rule, this simplifies to:
    \((7^4)^8 = 7^{4 \cdot 8} = 7^{32}\).

So, the expressions that are developed using the power rule of exponents are:

  • \((7^8) \cdot (7^{10})\) which simplifies to \(7^{18}\).
  • \((7^4)^8\) which simplifies to \(7^{32}\).

If the question is asking which expressions can be further simplified using the power rule, then options 3 and 4 are the ones that apply.

only one answer!

The expression that is correctly developed to use the power rule of exponents is:

\((7^8) \cdot (7^{10})\), which simplifies to \(7^{18}\).

thank you! ❤️

You're welcome! ❤️ If you have any more questions or need further assistance, feel free to ask!