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Popular >

simplify (9^{1/4})^{7/2}

Solution

simplify

(9^{\frac{1}{4}})^{\frac{7}{2}}

Solution

3 \cdot 3^{\frac{3}{4}}

+1

Decimal Notation

6.83852 \dots

Solution steps

(9^{\frac{1}{4}})^{\frac{7}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 9^{\frac{1}{4} \cdot \frac{7}{2}}

\frac{1}{4} \cdot \frac{7}{2} = \frac{7}{8}

= 9^{\frac{7}{8}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{7}{8}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{2 \cdot \frac{7}{8}}

2 \cdot \frac{7}{8} = \frac{7}{4}

= 3^{\frac{7}{4}}

3^{\frac{7}{4}} = 3^{1 + \frac{3}{4}}

= 3^{1 + \frac{3}{4}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 3^{1} \cdot 3^{\frac{3}{4}}

Refine

= 3 \cdot 3^{\frac{3}{4}}

Popular Examples

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(\frac{2}{3} + \frac{1}{12}) \cdot (\frac{7}{10} + \frac{1}{4})

6 m - 168 = - 6 m

Frequently Asked Questions (FAQ)

What is (9^{1/4})^{7/2} ?
The solution to (9^{1/4})^{7/2} is 3*3^{3/4}