Question

What is (4^5 )^2 (1 point) Responses 410 4 to the 10th power 47 4 to the 7th power 43 4 cubed 4 4 Question 2 What is (54ab)^0 (1 point) Responses 0 0 54ab 54ab 1 1 Question 3 What is a^7b^6/a^2b^4 (1 point) Responses a9b10 A to the 9th power b to the 10th power a5b2 A to the 5th power b squared a14b24 A to the 14th power b to the 24th power ab ab Question 4 10b^4 x 5b^2 (1 point) Responses 50b8 50 b to the 8th power 50b6 50 b to the 6th power 15b6 15 b to the 6th power 15b8 15 b to the 8th power Question 5 8t^52t^3 (1 point) Responses 4t2 4 t squared 10t2 10 t squared 4t15 4 t to the 15th power 6t2

Answer 1

Here are the solutions to each of your questions:

**Question 1:** What is \((4^5)^2\)?

Using the power of a power rule: \((a^m)^n = a^{m \cdot n}\)

\[
(4^5)^2 = 4^{5 \cdot 2} = 4^{10}
\]

**Response:** 4 to the 10th power

---

**Question 2:** What is \((54ab)^0\)?

Any non-zero number raised to the power of 0 is equal to 1.

**Response:** 1

---

**Question 3:** What is \(\frac{a^7b^6}{a^2b^4}\)?

To simplify, we use the rule \(\frac{a^m}{a^n} = a^{m-n}\):

\[
\frac{a^7}{a^2} = a^{7-2} = a^5
\]
\[
\frac{b^6}{b^4} = b^{6-4} = b^2
\]

So,
\[
\frac{a^7b^6}{a^2b^4} = a^5b^2
\]

**Response:** \(A\) to the 5th power \(b\) squared

---

**Question 4:** What is \(10b^4 \times 5b^2\)?

Multiply the coefficients and add the exponents of \(b\):

\[
10 \times 5 = 50
\]
\[
b^4 \times b^2 = b^{4+2} = b^6
\]

So,
\[
10b^4 \times 5b^2 = 50b^6
\]

**Response:** 50 \(b\) to the 6th power

---

**Question 5:** What is \(8t^5 \times 2t^3\)?

Again, multiply the coefficients and add the exponents of \(t\):

\[
8 \times 2 = 16
\]
\[
t^5 \times t^3 = t^{5+3} = t^8
\]

So,
\[
8t^5 \times 2t^3 = 16t^8
\]

None of the given responses match; however, the solution should be \(16t^8\).

Please let me know if you need any further explanations!