Answer :
To solve the expression [tex]\(5^0 \cdot 5^2\)[/tex], we can use the properties of exponents.
Here's a step-by-step solution:
1. Understand the Exponents:
- Any number raised to the power of 0 is 1. Therefore, [tex]\(5^0 = 1\)[/tex].
- [tex]\(5^2\)[/tex] means 5 multiplied by itself, so [tex]\(5^2 = 25\)[/tex].
2. Multiply the Results:
- Now, substitute these values back into the expression: [tex]\(1 \cdot 25\)[/tex].
- Calculating this gives us [tex]\(1 \times 25 = 25\)[/tex].
3. Identify the Equivalent Expression:
- The result of [tex]\(5^0 \cdot 5^2\)[/tex] is 25, and since [tex]\(5^2 = 25\)[/tex], the expression is equivalent to [tex]\(5^2\)[/tex].
Therefore, the choice that is equivalent to the expression [tex]\(5^0 \cdot 5^2\)[/tex] is D. [tex]\(5^2\)[/tex].
Here's a step-by-step solution:
1. Understand the Exponents:
- Any number raised to the power of 0 is 1. Therefore, [tex]\(5^0 = 1\)[/tex].
- [tex]\(5^2\)[/tex] means 5 multiplied by itself, so [tex]\(5^2 = 25\)[/tex].
2. Multiply the Results:
- Now, substitute these values back into the expression: [tex]\(1 \cdot 25\)[/tex].
- Calculating this gives us [tex]\(1 \times 25 = 25\)[/tex].
3. Identify the Equivalent Expression:
- The result of [tex]\(5^0 \cdot 5^2\)[/tex] is 25, and since [tex]\(5^2 = 25\)[/tex], the expression is equivalent to [tex]\(5^2\)[/tex].
Therefore, the choice that is equivalent to the expression [tex]\(5^0 \cdot 5^2\)[/tex] is D. [tex]\(5^2\)[/tex].