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!