Question

Eli claims that the product of 6⁵ and 5⁻³ is 6². Which explains whether Eli is correct?

A) Eli is correct. He added 5 + (-3) to find the exponent of 2.
B) Eli is incorrect. He added the exponents instead of subtracting them.
C) Eli is incorrect. He subtracted the exponents instead of adding them.
D) Eli is incorrect. He added the exponents even though the bases are not the same.

Answer 1

Eli is incorrect. The product of 6^5 and 5^-3 is 62.208. To find the product of two numbers with different exponents, you must multiply the base numbers and subtract the exponents.

Step-by-step explanation:

5-3 = 1/53 = 1/(5 x 5 x 5) = 1/125

65 = 6 x 6 x 6 x 6 x 6 = 7776

The product of 65 and 5-3 is 7776 x 1/125 = 62.208

Therefore, Eli is incorrect. To find the product of two numbers with different exponents, you must multiply the base numbers and subtract the exponents. Eli added the exponents instead of subtracting them.