College

Compare the expressions [tex]$62+4^4$[/tex] and [tex]$94+5^3$[/tex]. Which statement is correct?

A. [tex]$62+4^4=318$[/tex], which is greater than [tex]$94+5^3=109$[/tex].

B. [tex]$62+4^4=78$[/tex], which is less than [tex]$94+5^3=109$[/tex].

C. [tex]$62+4^4=318$[/tex], which is greater than [tex]$94+5^3=219$[/tex].

D. [tex]$62+4^4=78$[/tex], which is less than [tex]$94+5^3=219$[/tex].

Answer :

Sure! Let's evaluate each expression step by step and compare them.

First, we'll calculate the value of the expression [tex]\(62 + 4^4\)[/tex]:

1. Calculate [tex]\(4^4\)[/tex], which means [tex]\(4 \times 4 \times 4 \times 4\)[/tex].
- [tex]\(4 \times 4 = 16\)[/tex]
- [tex]\(16 \times 4 = 64\)[/tex]
- [tex]\(64 \times 4 = 256\)[/tex]

2. Add 62 to the result from step 1:
- [tex]\(62 + 256 = 318\)[/tex]

So, the value of [tex]\(62 + 4^4\)[/tex] is 318.

Now, let's calculate the value of the expression [tex]\(94 + 5^3\)[/tex]:

1. Calculate [tex]\(5^3\)[/tex], which means [tex]\(5 \times 5 \times 5\)[/tex].
- [tex]\(5 \times 5 = 25\)[/tex]
- [tex]\(25 \times 5 = 125\)[/tex]

2. Add 94 to the result from step 1:
- [tex]\(94 + 125 = 219\)[/tex]

So, the value of [tex]\(94 + 5^3\)[/tex] is 219.

Finally, let's compare the two results:
- [tex]\(318 > 219\)[/tex]

Therefore, the correct statement is:
[tex]\(62 + 4^4 = 318\)[/tex], which is greater than [tex]\(94 + 5^3 = 219\)[/tex].