Question

Find the equivalent expression using the same bases.

a) (92^47)
b) (9^247)
c) (9247^1)
d) (9^2^47)

Answer 1

Final answer:

The equivalent expression for the given numbers, using base 9 when possible, are (9^2)^47 = 9^94 and 9^247. The expression 9247^1 does not conform to base 9 and therefore is not comparable to the others in terms of rewriting with a common base.

Step-by-step explanation:

The student is asking for the equivalent expression using the same bases. To rewrite these all with the base 9, we have the following:

• (92)47 = 92 × 47 = 994

• 9247 is already with the base 9.

• 92471 is not a power of 9 and cannot be rewritten in the same form as the others.

• (92)47 is already provided in part a) as 994.

Here the scientific notation is not directly relevant since we are dealing with rewriting exponents, but it's a useful tool for handling large numbers.

To evaluate expressions, we can use calculators and express the final answers in scientific notation if necessary.