Question

Evaluate the variable expression when x = – 4

4x² ÷(– 10)

Short answer

The value of4x² ÷ (– 10) after evaluating the power is – 6.4 when x = – 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

Find the base and exponent of 27 and evaluate

Example: Find the base and the exponent of 2⁷ and evaluate the value.

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

a = 2 and x = 7

Base = 2 and exponent = 7

Evaluate: $2^7=2 · 2 · 2 · 2 · 2 · 2 · 2 =128$

Evaluate the expression 4x2 ÷ (– 10) when x = – 4 

Evaluate the expression 4x² ÷ (– 10) when x = – 4

According to the exponent rule:

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

a = x and x = 2

In repeated multiplication:$x^2 = x · x$

Rule:The product of two negative integers is positive and quotient of a positive and a negative integer is negative.

When x = – 4:$\frac{4 x^2}{- 10} = \frac{4 · x · x}{- 10} = \frac{4 · (- 4) · (- 4)}{- 10}= \frac{64}{- 10}= - 6.4$

The value of4x² ÷ (– 10) after evaluating the power is – 6.4 when x = – 4.