The solution to sqrt(9)^7 is 2187

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simplify sqrt(9)^7

Solution

simplify

9^{7}

2187

Solution steps

(9)^{7}

Apply exponent rule:

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

(9)^{6 + 1} = (9)^{6} 9

= (9)^{6} 9

(9)^{6} = ((9)^{2})^{3}

= ((9)^{2})^{3} 9

Apply exponent rule:

(9)^{2} = 9

= 9^{3} 9

Apply radical rule:

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

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

= 9^{3} \cdot 9^{\frac{1}{2}}

Apply exponent rule:

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

9^{3} \cdot 9^{\frac{1}{2}} = 9^{3 + \frac{1}{2}}

= 9^{3 + \frac{1}{2}}

3 + \frac{1}{2} = \frac{7}{2}

= 9^{\frac{7}{2}}

Factor the number:

9 = 3^{2}

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

Apply exponent rule:

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

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

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

= 3^{7}

3^{7} = 2187

= 2187

(x + 4) (x - 1)

4.03704 \cdot \frac{1 0 ^{- 19}}{1.05457} \cdot 1 0^{- 34}

0.8 \cdot 1 0^{- 7}

0.8 \cdot 1 0^{- 3}