Answer:
24,300,000
Step-by-step explanation:
Given expression: [tex](5 \cdot 5 + 5)^5[/tex]
We can solve this following the order of operations (PEDMAS):
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
We need to carry out that which is in the parentheses first: [tex]5 \cdot 5 + 5[/tex]
According to the order of operations, we should carry out the multiplication first, followed by the addition:
[tex]\implies 5 \cdot 5+5=25+5=30[/tex]
Therefore,
[tex](5 \cdot 5 + 5)^5=(30)^5[/tex]
Finally, we carry out the exponent:
[tex]\begin{aligned}\implies 30^5 &=30 \cdot 30 \cdot 30 \cdot 30 \cdot 30\\ & =24,300,000\end{aligned}[/tex]
Therefore,
[tex](5 \cdot 5 + 5)^5=24,300,000[/tex]
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Alternatively, if the expression is [tex]5 \cdot 5 + 5^5[/tex]
We would carry out the exponent first:
[tex]\begin{aligned}\implies 5 \cdot 5 + 5^5 &=5 \cdot 5+(5 \cdot 5 \cdot 5 \cdot 5 \cdot 5)\\ & =5 \cdot 5+3125\end{aligned}[/tex]
Then the multiplication:
[tex]\implies 5 \cdot 5+3125=25+3125[/tex]
And finally the addition:
[tex]\implies 25+3125=3150[/tex]
Therefore,
[tex]5 \cdot 5 + 5^5=3150[/tex]
