Let's solve each of the questions step-by-step:
Question 1: What is \( 5^7 \times 5^8 \)?
To solve this, you can use the property of exponents which states that when you multiply two powers with the same base, you add their exponents: \[ 5^7 \times 5^8 = 5^{7+8} = 5^{15} \] So the answer is 5 to the 15th power.
Question 2: What is \( \frac{8^5}{8^2} \)?
For division with the same base, you subtract the exponents: \[ \frac{8^5}{8^2} = 8^{5-2} = 8^3 \] So the answer is 8 cubed.
Question 3: What is \( (7c^3)(8c^2) \)?
When multiplying terms, you multiply the coefficients (the numbers in front) and add the exponents of the like bases: \[ (7 \times 8)(c^{3+2}) = 56c^5 \] So the answer is 56c to the 5th power.
Question 4: What is \( 859^1 \)?
Any number raised to the power of 1 is the number itself: \[ 859^1 = 859 \] So the answer is 859.
Summary of Answers:
- 5 to the 15th power
- 8 cubed
- 56c to the 5th power
- 859