1Cademy - Simplifying $$4^3$$, $$7^1$$, $$\left(\frac{5}{6}\right)^2$$, and $$(0.63)^2$$

Learn Before

Exponential Notation in Algebra

Example

Simplifying $4^3$ , $7^1$ , $\left(\frac{5}{6}\right)^2$ , and $(0.63)^2$

Applying the definition of exponents to four expressions with different types of bases demonstrates that the expand-and-multiply procedure works regardless of whether the base is a whole number, a fraction, or a decimal:

ⓐ $4^3 = 64$ : The exponent $3$ directs us to use the base $4$ as a factor three times. Expand and multiply: $4 \cdot 4 \cdot 4 = 64$ .

ⓑ $7^1 = 7$ : The exponent $1$ means the base appears as a factor only once, so $7^1 = 7$ . Any number raised to the first power equals itself.

ⓒ $\left(\frac{5}{6}\right)^2 = \frac{25}{36}$ : The exponent $2$ tells us to multiply two factors of the fraction $\frac{5}{6}$ . Multiply the numerators and the denominators: $\frac{5}{6} \cdot \frac{5}{6} = \frac{25}{36}$ .

ⓓ $(0.63)^2 = 0.3969$ : The exponent $2$ tells us to multiply two factors of the decimal $0.63$ : $(0.63)(0.63) = 0.3969$ .

These four parts illustrate that the same procedure — expanding the exponent into repeated multiplication of the base and then computing the product — applies uniformly to whole numbers, fractions, and decimals.

Updated 2026-04-21

Contributors are:

Who are from:

References

OpenStax Elementary Algebra

Learn Before

Related

Learn After