To solve the expression [tex]\(\left(\frac{5}{4}\right)^3\)[/tex], follow these steps:
1. Identify the Base and the Exponent:
The base in the expression is [tex]\(\frac{5}{4}\)[/tex] and the exponent is 3.
2. Understand the Meaning of the Exponent:
Raising a number to the power of 3 means multiplying the number by itself three times.
3. Write the Expression Accordingly:
[tex]\[
\left(\frac{5}{4}\right)^3 = \frac{5}{4} \times \frac{5}{4} \times \frac{5}{4}
\][/tex]
4. Multiply the Numerators:
Multiply the numerators (top parts of the fractions):
[tex]\[
5 \times 5 \times 5 = 125
\][/tex]
5. Multiply the Denominators:
Multiply the denominators (bottom parts of the fractions):
[tex]\[
4 \times 4 \times 4 = 64
\][/tex]
6. Form the New Fraction:
The expression [tex]\(\left(\frac{5}{4}\right)^3\)[/tex] now becomes one fraction:
[tex]\[
\frac{125}{64}
\][/tex]
7. Convert the Fraction to a Decimal (if needed):
Divide the numerator by the denominator to convert the fraction to a decimal:
[tex]\[
\frac{125}{64} \approx 1.953125
\][/tex]
So, [tex]\(\left(\frac{5}{4}\right)^3 = 1.953125\)[/tex].
