Question Simplify $(w^{1/2})^{2/5}$ and write the answer in exponential form.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}}$ .
2. We need to simplify the expression and write the answer in exponential form.

STEP 2

To simplify the expression, we will use the power of a power rule, which states that $\left(a^{m}\right)^{n} = a^{m \cdot n}$ .

STEP 3

Apply the power of a power rule to the given expression.
$\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}} = w^{\frac{1}{2} \cdot \frac{2}{5}}$

STEP 4

Multiply the exponents to simplify the expression further.
$w^{\frac{1}{2} \cdot \frac{2}{5}} = w^{\frac{1 \cdot 2}{2 \cdot 5}}$

STEP 5

Simplify the fraction by multiplying the numerators and the denominators.
$w^{\frac{1 \cdot 2}{2 \cdot 5}} = w^{\frac{2}{10}}$

STEP 6

Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$w^{\frac{2}{10}} = w^{\frac{2 \div 2}{10 \div 2}}$

STEP 7

Complete the simplification of the fraction.
$w^{\frac{2 \div 2}{10 \div 2}} = w^{\frac{1}{5}}$
The expression simplified in exponential form is $w^{\frac{1}{5}}$ .

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Question Simplify $(w^{1/2})^{2/5}$ and write the answer in exponential form.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}}$ .
2. We need to simplify the expression and write the answer in exponential form.

STEP 2

To simplify the expression, we will use the power of a power rule, which states that $\left(a^{m}\right)^{n} = a^{m \cdot n}$ .

STEP 3

Apply the power of a power rule to the given expression.
$\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}} = w^{\frac{1}{2} \cdot \frac{2}{5}}$

STEP 4

Multiply the exponents to simplify the expression further.
$w^{\frac{1}{2} \cdot \frac{2}{5}} = w^{\frac{1 \cdot 2}{2 \cdot 5}}$

STEP 5

Simplify the fraction by multiplying the numerators and the denominators.
$w^{\frac{1 \cdot 2}{2 \cdot 5}} = w^{\frac{2}{10}}$

STEP 6

Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$w^{\frac{2}{10}} = w^{\frac{2 \div 2}{10 \div 2}}$

STEP 7

Complete the simplification of the fraction.
$w^{\frac{2 \div 2}{10 \div 2}} = w^{\frac{1}{5}}$
The expression simplified in exponential form is $w^{\frac{1}{5}}$ .

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Question Simplify (w1/2)2/5(w^{1/2})^{2/5}(w1/2)2/5 and write the answer in exponential form.

Studdy Solution

STEP 1

Assumptions1. We are given the expression (w12)25\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}}(w21​)52​.2. We need to simplify the expression and write the answer in exponential form.

STEP 2

To simplify the expression, we will use the power of a power rule, which states that (am)n=am⋅n\left(a^{m}\right)^{n} = a^{m \cdot n}(am)n=am⋅n.

STEP 3

Apply the power of a power rule to the given expression.(w12)25=w12⋅25\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}} = w^{\frac{1}{2} \cdot \frac{2}{5}}(w21​)52​=w21​⋅52​

STEP 4

Multiply the exponents to simplify the expression further.w12⋅25=w1⋅22⋅5w^{\frac{1}{2} \cdot \frac{2}{5}} = w^{\frac{1 \cdot 2}{2 \cdot 5}}w21​⋅52​=w2⋅51⋅2​

STEP 5

Simplify the fraction by multiplying the numerators and the denominators.w1⋅22⋅5=w210w^{\frac{1 \cdot 2}{2 \cdot 5}} = w^{\frac{2}{10}}w2⋅51⋅2​=w102​

STEP 6

Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2.w210=w2÷210÷2w^{\frac{2}{10}} = w^{\frac{2 \div 2}{10 \div 2}}w102​=w10÷22÷2​

STEP 7

Complete the simplification of the fraction.w2÷210÷2=w15w^{\frac{2 \div 2}{10 \div 2}} = w^{\frac{1}{5}}w10÷22÷2​=w51​The expression simplified in exponential form is w15w^{\frac{1}{5}}w51​.

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Question Simplify $(w^{1/2})^{2/5}$ and write the answer in exponential form.

Assumptions
1. We are given the expression $\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}}$ .
2. We need to simplify the expression and write the answer in exponential form.

To simplify the expression, we will use the power of a power rule, which states that $\left(a^{m}\right)^{n} = a^{m \cdot n}$ .

Apply the power of a power rule to the given expression.
$\left(w^{\frac{1}{2}}\right)^{\frac{2}{5}} = w^{\frac{1}{2} \cdot \frac{2}{5}}$

Multiply the exponents to simplify the expression further.
$w^{\frac{1}{2} \cdot \frac{2}{5}} = w^{\frac{1 \cdot 2}{2 \cdot 5}}$

Simplify the fraction by multiplying the numerators and the denominators.
$w^{\frac{1 \cdot 2}{2 \cdot 5}} = w^{\frac{2}{10}}$

Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$w^{\frac{2}{10}} = w^{\frac{2 \div 2}{10 \div 2}}$

Complete the simplification of the fraction.
$w^{\frac{2 \div 2}{10 \div 2}} = w^{\frac{1}{5}}$
The expression simplified in exponential form is $w^{\frac{1}{5}}$ .