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Popular >

simplify (sqrt(9))^5

Solution

simplify

(9)^{5}

Solution

243

Solution steps

(9)^{5}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(9)^{4 + 1} = (9)^{4} 9

= (9)^{4} 9

(9)^{4} = ((9)^{2})^{2}

= ((9)^{2})^{2} 9

Apply exponent rule:

(9)^{2} = 9

= 9^{2} 9

Apply radical rule:

a = a^{\frac{1}{2}}

9 = 9^{\frac{1}{2}}

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

9^{2} \cdot 9^{\frac{1}{2}} = 9^{2 + \frac{1}{2}}

= 9^{2 + \frac{1}{2}}

2 + \frac{1}{2} = \frac{5}{2}

= 9^{\frac{5}{2}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{5}{2}}

Apply exponent rule:

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

= 3^{2 \cdot \frac{5}{2}}

2 \cdot \frac{5}{2} = 5

= 3^{5}

3^{5} = 243

= 243

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Frequently Asked Questions (FAQ)

What is (sqrt(9))^5 ?
The solution to (sqrt(9))^5 is 243