Solved on Mar 04, 2024

Rewrite the expression as a single fraction. $(\frac{1}{5})^{3}=\frac{1}{125}$

STEP 1

Assumptions
1. We are given the expression $\left(\frac{1}{5}\right)^{3}$ .
2. We need to rewrite this expression as a single fraction.
3. The numerator of the fraction has already been rewritten as 1 because $1 \cdot 1 \cdot 1$ equals 1.

STEP 2

Understand the exponent rule for fractions. When a fraction is raised to a power, both the numerator and the denominator are raised to that power.
$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

STEP 3

Apply the exponent rule to the given expression.
$\left(\frac{1}{5}\right)^{3} = \frac{1^3}{5^3}$

STEP 4

Calculate the numerator of the fraction.
$1^3 = 1$

STEP 5

Calculate the denominator of the fraction.
$5^3 = 5 \cdot 5 \cdot 5$

STEP 6

Compute the value of $5^3$ .
$5^3 = 5 \cdot 5 \cdot 5 = 125$

STEP 7

Combine the numerator and the denominator to form the single fraction.
$\left(\frac{1}{5}\right)^{3} = \frac{1}{125}$
Therefore, the expression $\left(\frac{1}{5}\right)^{3}$ can be rewritten as $\frac{1}{125}$ , and the square in the original problem statement should be filled with the number 125.
$\left(\frac{1}{5}\right)^{3}=\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5}=\frac{1}{125}$

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Rewrite the expression as a single fraction. $(\frac{1}{5})^{3}=\frac{1}{125}$

STEP 1

Assumptions
1. We are given the expression $\left(\frac{1}{5}\right)^{3}$ .
2. We need to rewrite this expression as a single fraction.
3. The numerator of the fraction has already been rewritten as 1 because $1 \cdot 1 \cdot 1$ equals 1.

STEP 2

Understand the exponent rule for fractions. When a fraction is raised to a power, both the numerator and the denominator are raised to that power.
$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

STEP 3

Apply the exponent rule to the given expression.
$\left(\frac{1}{5}\right)^{3} = \frac{1^3}{5^3}$

STEP 4

Calculate the numerator of the fraction.
$1^3 = 1$

STEP 5

Calculate the denominator of the fraction.
$5^3 = 5 \cdot 5 \cdot 5$

STEP 6

Compute the value of $5^3$ .
$5^3 = 5 \cdot 5 \cdot 5 = 125$

STEP 7

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Rewrite the expression as a single fraction. (15)3=1125(\frac{1}{5})^{3}=\frac{1}{125}(51​)3=1251​

STEP 1

Assumptions1. We are given the expression (15)3\left(\frac{1}{5}\right)^{3}(51​)3.2. We need to rewrite this expression as a single fraction.3. The numerator of the fraction has already been rewritten as 1 because 1⋅1⋅11 \cdot 1 \cdot 11⋅1⋅1 equals 1.

STEP 2

Understand the exponent rule for fractions. When a fraction is raised to a power, both the numerator and the denominator are raised to that power.(ab)n=anbn\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}(ba​)n=bnan​

STEP 3

Apply the exponent rule to the given expression.(15)3=1353\left(\frac{1}{5}\right)^{3} = \frac{1^3}{5^3}(51​)3=5313​

STEP 4

Calculate the numerator of the fraction.13=11^3 = 113=1

STEP 5

Calculate the denominator of the fraction.53=5⋅5⋅55^3 = 5 \cdot 5 \cdot 553=5⋅5⋅5

STEP 6

Compute the value of 535^353.53=5⋅5⋅5=1255^3 = 5 \cdot 5 \cdot 5 = 12553=5⋅5⋅5=125

STEP 7

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Rewrite the expression as a single fraction. $(\frac{1}{5})^{3}=\frac{1}{125}$

Assumptions
1. We are given the expression $\left(\frac{1}{5}\right)^{3}$ .
2. We need to rewrite this expression as a single fraction.
3. The numerator of the fraction has already been rewritten as 1 because $1 \cdot 1 \cdot 1$ equals 1.

Understand the exponent rule for fractions. When a fraction is raised to a power, both the numerator and the denominator are raised to that power.
$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

Apply the exponent rule to the given expression.
$\left(\frac{1}{5}\right)^{3} = \frac{1^3}{5^3}$

Calculate the numerator of the fraction.
$1^3 = 1$

Calculate the denominator of the fraction.
$5^3 = 5 \cdot 5 \cdot 5$

Compute the value of $5^3$ .
$5^3 = 5 \cdot 5 \cdot 5 = 125$