Question

Evaluate the expression when n = 7 and n = 0.4.

n⁵

Short answer

The value of $n^5$after evaluating the power is 16807 when n = 7 and 0.01024 when n = 0.4

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 and evaluate 

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

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

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: $5^4 = 5 · 5 · 5 · 5 = 625$

Evaluate the expression n5 when n = 7 and n = 0.4 

Evaluate the expression $n^5$ whenn = 7 and n = 0.4.

According to the exponent rule:

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

a = n and x = 5

In repeated multiplication:$n^4 = n · n · n · n$

When n = 7:$n^4 = n · n · n · n= 7 · 7 · 7 · 7=2401$

When n = 0.4:$n^4 = n · n · n · n= 0.4 · 0.4 · 0.4 · 0.4=0.0256$

The value of $n^5$after evaluating the power is 16807 when n = 7 and 0.01024 when n = 0.4