Question

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

n³

Short answer

The value of $n^3$after evaluating the power is 343 when n = 7 and 0.064 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 · 5 in 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 n3 when n = 7 and n = 0.4 

Evaluate the expression $n^3$ 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 = 3

In repeated multiplication:$n^3 = n · n · n$

When n = 7:$n^3 = n · n · n = 7 · 7 · 7 =343$

When n = 0.4:$n^3 = n · n · n = 0.4 · 0.4 · 0.4 =0.064$

The value of $n^3$after evaluating the power is 343 when n = 7 and 0.064 when n = 0.4