Math / Algebra

QuestionSimplify. $\frac{8 u^{2}}{48 u^{5}}$

Studdy Solution

STEP 1

1. We are asked to simplify the given expression.
2. The expression involves division of monomials.
3. Simplification involves reducing coefficients and applying the laws of exponents.

STEP 2

1. Simplify the coefficients in the fraction.
2. Apply the laws of exponents to simplify the variable terms.

STEP 3

Identify the coefficients in the fraction $\frac{8}{48}$ and simplify them by finding the greatest common divisor (GCD).
The GCD of 8 and 48 is 8. Therefore, simplify the fraction:
$\frac{8}{48} = \frac{8 \div 8}{48 \div 8} = \frac{1}{6}$

STEP 4

Apply the laws of exponents to simplify the variable terms $\frac{u^{2}}{u^{5}}$ .
According to the laws of exponents, $\frac{u^{a}}{u^{b}} = u^{a-b}$ .
$\frac{u^{2}}{u^{5}} = u^{2-5} = u^{-3}$

STEP 5

Combine the simplified coefficient and the simplified variable term:
$\frac{1}{6} \times u^{-3} = \frac{1}{6u^{3}}$
The simplified expression is:
$\boxed{\frac{1}{6u^{3}}}$

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QuestionSimplify. $\frac{8 u^{2}}{48 u^{5}}$

Studdy Solution

STEP 1

1. We are asked to simplify the given expression.
2. The expression involves division of monomials.
3. Simplification involves reducing coefficients and applying the laws of exponents.

STEP 2

1. Simplify the coefficients in the fraction.
2. Apply the laws of exponents to simplify the variable terms.

STEP 3

Identify the coefficients in the fraction $\frac{8}{48}$ and simplify them by finding the greatest common divisor (GCD).
The GCD of 8 and 48 is 8. Therefore, simplify the fraction:
$\frac{8}{48} = \frac{8 \div 8}{48 \div 8} = \frac{1}{6}$

STEP 4

Apply the laws of exponents to simplify the variable terms $\frac{u^{2}}{u^{5}}$ .
According to the laws of exponents, $\frac{u^{a}}{u^{b}} = u^{a-b}$ .
$\frac{u^{2}}{u^{5}} = u^{2-5} = u^{-3}$

STEP 5

Combine the simplified coefficient and the simplified variable term:
$\frac{1}{6} \times u^{-3} = \frac{1}{6u^{3}}$
The simplified expression is:
$\boxed{\frac{1}{6u^{3}}}$

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QuestionSimplify. 8u248u5\frac{8 u^{2}}{48 u^{5}}48u58u2​

Studdy Solution

STEP 1

1. We are asked to simplify the given expression.2. The expression involves division of monomials.3. Simplification involves reducing coefficients and applying the laws of exponents.

STEP 2

1. Simplify the coefficients in the fraction.2. Apply the laws of exponents to simplify the variable terms.

STEP 3

Identify the coefficients in the fraction 848\frac{8}{48}488​ and simplify them by finding the greatest common divisor (GCD).The GCD of 8 and 48 is 8. Therefore, simplify the fraction:848=8÷848÷8=16 \frac{8}{48} = \frac{8 \div 8}{48 \div 8} = \frac{1}{6} 488​=48÷88÷8​=61​

STEP 4

Apply the laws of exponents to simplify the variable terms u2u5\frac{u^{2}}{u^{5}}u5u2​.According to the laws of exponents, uaub=ua−b\frac{u^{a}}{u^{b}} = u^{a-b}ubua​=ua−b.u2u5=u2−5=u−3 \frac{u^{2}}{u^{5}} = u^{2-5} = u^{-3} u5u2​=u2−5=u−3

STEP 5

Combine the simplified coefficient and the simplified variable term:16×u−3=16u3 \frac{1}{6} \times u^{-3} = \frac{1}{6u^{3}} 61​×u−3=6u31​The simplified expression is:16u3 \boxed{\frac{1}{6u^{3}}} 6u31​​

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QuestionSimplify. $\frac{8 u^{2}}{48 u^{5}}$

1. We are asked to simplify the given expression.
2. The expression involves division of monomials.
3. Simplification involves reducing coefficients and applying the laws of exponents.

1. Simplify the coefficients in the fraction.
2. Apply the laws of exponents to simplify the variable terms.

Identify the coefficients in the fraction $\frac{8}{48}$ and simplify them by finding the greatest common divisor (GCD).
The GCD of 8 and 48 is 8. Therefore, simplify the fraction:
$\frac{8}{48} = \frac{8 \div 8}{48 \div 8} = \frac{1}{6}$

Apply the laws of exponents to simplify the variable terms $\frac{u^{2}}{u^{5}}$ .
According to the laws of exponents, $\frac{u^{a}}{u^{b}} = u^{a-b}$ .
$\frac{u^{2}}{u^{5}} = u^{2-5} = u^{-3}$

Combine the simplified coefficient and the simplified variable term:
$\frac{1}{6} \times u^{-3} = \frac{1}{6u^{3}}$
The simplified expression is:
$\boxed{\frac{1}{6u^{3}}}$