Which expression is correctly developed to use the Power Rule of Exponents? 12^9 (7^4)^8 (−5)^0 (7^8)⋅(7^10)

Answer 1

To use the Power Rule of Exponents effectively, we need to identify which of the expressions can be simplified using the Power Rule. The Power Rule states that $(a^m{)}^n=a^{m\cdot n}$, and for multiplication, it states that $a^m\cdot a^n=a^{m+n}$.

Let's analyze the given expressions:

1. ${12}^9$ - This expression is already in the simplest form and doesn't invoke the Power Rule.

2. $(7^4{)}^8$ - This can be simplified using the Power Rule: $$(7^4{)}^8=7^{4\cdot 8}=7^{32}.$$

3. $(-5{)}^0$ - This expression evaluates to 1, since any non-zero number raised to the power of 0 is 1. It does not involve using the Power Rule as stated.

4. $(7^8)\cdot (7^{10})$ - This can also be simplified using the multiplication rule: $$(7^8)\cdot (7^{10})=7^{8+10}=7^{18}.$$

Thus, the expressions that are correctly developed using the Power Rule are $(7^4{)}^8$ and $(7^8)\cdot (7^{10})$.

If you're looking for the expression that explicitly shows the use of the Power Rule, then $(7^4{)}^8$ is a direct application of the rule $(a^m{)}^n$. On the other hand, $(7^8)\cdot (7^{10})$ exemplifies the product rule for exponents. Therefore, both expressions accurately apply exponent rules, but in the context of the Power Rule specifically, $(7^4{)}^8$ is the clearest instance.

Answer 2

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Answer 3

Sure! Based on the expressions provided, the one that correctly demonstrates the use of the Power Rule of Exponents is:

(7^4)^8

This expression can be simplified using the Power Rule:

$$(7^4{)}^8=7^{4\cdot 8}=7^{32}.$$

Answer 4

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Answer 5

Thank you so much for your kind words! I'm glad I could help. If you have any more questions or need assistance with anything else, feel free to ask!

Answer 6

What exponent would make the two expressions equivalent: (3^3)^x=3^24 ?(1 point) Responses 15 8 21 27

Answer 7

To find the value of $x$ that makes the two expressions equivalent, we can use the Power Rule of Exponents:

$$(3^3{)}^x=3^{3x}$$

Setting this equal to the right side of the equation:

$$3^{3x}=3^{24}$$

Since the bases are the same, we can set the exponents equal to each other:

$$3x=24$$

Now, solve for $x$:

$$x=\frac{24}{3}=8$$

Thus, the value of $x$ that makes the expressions equivalent is 8.