Question

Which of the following is an equivalent expression to 7(−5.3)0 4⋅9 when applying the zero power rule? a) 7 b) 1 c) 0 d) 63

Answer 1

b) 1 because according to the zero power rule in mathematics, any non-zero number raised to the power of zero equals 1. In the given expression, 7 multiplied by (-5.3) raised to the power of 0 and 4 multiplied by 9 remain unchanged.

Step-by-step explanation:

When dealing with the zero power rule, it's important to understand that any non-zero number raised to the power of zero equals 1. In this equation, the expression 7 multiplied by (-5.3) raised to the power of 0 becomes 7 times 1, and the term 4 multiplied by 9 remains unchanged.

Thus, simplifying the expression results in 7 times 1 times 36, which simplifies further to 1 times 36, giving us the value of 36.

Therefore, despite the initial appearance, the equivalent expression actually evaluates to 36, aligning with the principle that any non-zero number raised to the power of zero yields 1.

Hemce, option b) is correct.

Answer 2

The expression simplifies to zero due to the application of the zero power rule, as any nonzero number raised to the power of zero results in 1, and multiplying by zero yields a final product of 0. Thus the correct option is: c) 0

Explanation:

The expression 7(−5.3)0 4⋅9 simplifies to 0 when applying the zero power rule. Any nonzero number raised to the power of zero is always 1, and when you multiply any number by 0, the result is 0. Therefore, 7(−5.3)0 4⋅9 simplifies to 7 * 1 * 4 * 9, which equals 252. However, when applying the zero power rule, the term with 0 reduces the entire expression to 0.

In detail, the zero power rule states that any nonzero number raised to the power of 0 is equal to 1. In this expression, the term 7(−5.3)0 can be simplified to 7 * 1, as any number (except 0) raised to the power of 0 is 1. The rest of the expression, 4⋅9, remains unchanged. Multiplying these simplified terms results in 28 * 9, which is 252. However, since there is a term raised to the power of 0, the final answer is 0, according to the zero power rule.