Examples with solutions for Applying Combined Exponents Rules: The power of zero

Exercise #1

Solve the following problem:

70= 7^0=

Step-by-Step Solution

To solve the problem of finding 70 7^0 , we will follow these steps:

  • Step 1: Identify the general rule for exponents with zero.

  • Step 2: Apply the rule to the given problem.

  • Step 3: Consider the provided answer choices and select the correct one.

Now, let's work through each step:

Step 1: A fundamental rule in exponents is that any non-zero number raised to the power of zero is equal to one. This can be expressed as: a0=1 a^0 = 1 where a a is not zero.

Step 2: Apply this rule to the problem: Since we have 70 7^0 , and 7 7 is certainly a non-zero number, the expression evaluates to 1. Therefore, 70=1 7^0 = 1 .

Therefore, the solution to the problem is 70=1 7^0 = 1 , which corresponds to choice 2.

Answer

1 1

Exercise #2

Solve the following problem:

(3)0= \left(-3\right)^0=

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Understand the zero exponent rule.

  • Apply this rule to the given expression.

  • Identify the correct answer from the given options.

According to the rule of exponents, any non-zero number raised to the power of zero is equal to 11. This is one of the fundamental properties of exponents.
Now, apply this rule:

Step 1: We are given the expression (3)0(-3)^0.
Step 2: Here, 3-3 is our base. We apply the zero exponent rule, which tells us that (3)0=1(-3)^0 = 1.

Therefore, the value of (3)0(-3)^0 is 11.

Answer

1 1

Exercise #3

1120=? 112^0=\text{?}

Video Solution

Step-by-Step Solution

We use the zero exponent rule.

X0=1 X^0=1 We obtain

1120=1 112^0=1 Therefore, the correct answer is option C.

Answer

1