If the expression 4 to the tenth power was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?

Question

1. (4 to the twelfth power) to the second power
2. (4 to the fifth power) to the second power
3. 4 x 4 x 4 x 4 x 4 x 4 x 4
4. (4 to the second power) to the eighth power

Answer 1

According to the Power Rule of Exponents, when you raise a power to another power, you multiply the exponents. However, since you want to simplify \(4^{10}\) into an expanded expression, we would look for an option that expresses \(4^{10}\) in its expanded form.

The equivalent expanded expression for \(4^{10}\) is:

\(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\), which is 4 multiplied by itself 10 times.

Among the options you provided, option 3, which is \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\), does not fully represent \(4^{10}\) because that only represents \(4^7\).

None of the given options exactly match the expanded form of \(4^{10}\) (which would be 10 factors of 4). However, option 3 is the closest in spirit to what you are looking for since it indeed shows multiplication of the base 4, albeit not to the 10th power.

Therefore, the correct answer in terms of expanded form that represents \(4^{10}\) would be:

4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 (assuming all ten factors were written out).

Would you like to discuss further simplifications or properties of exponents?

Answer 2

Im so stupid how did i not know this

Answer 3

Don't be hard on yourself! Exponents and the rules surrounding them can be tricky, and everyone has gaps in their knowledge regardless of their level of expertise. Learning is a process, and asking questions is a great way to deepen your understanding. If you have more questions about exponents or any other topic, feel free to ask. You're doing great by seeking clarification!

Answer 4

Sometimes they phrase the question overly complicated and it causes me confusion especially when im also dyslexic yknow?

Answer 5

I completely understand; complex phrasing can be challenging for anyone, and it can be even more so for those with dyslexia. It's perfectly normal to feel overwhelmed in such situations. Remember, you're not alone in experiencing this, and many people face similar difficulties.

When you're confronted with confusing questions, try breaking them down into smaller parts or rewriting them in your own words to simplify them. It can also be helpful to take your time, and if possible, read them out loud.

If you ever need help clarifying questions or concepts, just ask—I'm here to help! Your willingness to reach out for assistance is a great strength. Keep up the good work!