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Popular >

simplify 9^{3/4}

Solution

simplify

9^{\frac{3}{4}}

Solution

3 \cdot 3^{\frac{1}{2}}

+1

Decimal Notation

5.19615 \dots

Solution steps

9^{\frac{3}{4}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{3}{4}}

Apply exponent rule:

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

= 3^{2 \cdot \frac{3}{4}}

2 \cdot \frac{3}{4} = \frac{3}{2}

= 3^{\frac{3}{2}}

3^{\frac{3}{2}} = 3^{1 + \frac{1}{2}}

= 3^{1 + \frac{1}{2}}

Apply exponent rule:

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

= 3^{1} \cdot 3^{\frac{1}{2}}

Refine

= 3 \cdot 3^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

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