Question

Critical thinking Evaluate each power 0², 0³, 0⁴. Use your results to write a rule for the value of 0 raised to any nonzero whole number exponent.

Short answer

The value of 0 raised to any nonzero whole number exponent is always zero.

Step-by-step solution

– Explanation of the exponent formula

${\text{a}}^{\text{x}}\to$a is the base and x is exponent.

The power is the result of repeated multiplication of the same factor.

The expressionsa^xthis means that a has been used as a factor x times.

Write the product 5 · 5 · 5 · 5in exponent. 

Example: Write the product $5 · 5 · 5 · 5$in exponent.

Rule: ${\text{a}}^{\text{x}}\to$a is called base and x is exponent.

For:$5 · 5 · 5 · 5$:the base a = 5 and multiplied by 4 times.

In repeated multiplication: $5 · 5 · 5 · 5$in exponent form $5^4$

Evaluate each power 02, 03, 04, use your results to write a rule for the value of 0 raised to any nonzero whole number exponent.

Rule: ${\text{a}}^{\text{x}}\to$a is called base and x is exponent.

For:0², here base is 0 and multiplied 2 times.

To express the power in words, write:0raised to the power 2.

In repeated form and evaluate: $0^2=0 · 0 = 0$

For:0³, here base is 0 and multiplied 3 times.

To express the power in words, write:0raised to the power 3.

In repeated form and evaluate: $0^3=0 · 0 · 0= 0$

For:0⁴, here base is 0 and multiplied 4 times.

To express the power in words, write:0raised to the power 4.

In repeated form and evaluate: $0^4=0 · 0 · 0 · 0= 0$

By using all these values, we can conclude the value of 0 raised to any nonzero whole number exponent is always zero.