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Popular >

simplify sqrt(12)^7

Solution

simplify

12^{7}

Solution

34563

+1

Decimal Notation

5985.96759 \dots

Solution steps

(12)^{7}

Apply exponent rule:

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

(12)^{6 + 1} = (12)^{6} 12

= (12)^{6} 12

(12)^{6} = ((12)^{2})^{3}

= ((12)^{2})^{3} 12

Apply exponent rule:

(12)^{2} = 12

= 1 2^{3} 12

Apply radical rule:

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

12 = 1 2^{\frac{1}{2}}

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

Apply exponent rule:

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

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

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

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

= 1 2^{\frac{7}{2}}

Prime factorization of

12 : 2^{2} \cdot 3

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

(2^{2})^{\frac{7}{2}} = 128

= 128 \cdot 3^{\frac{7}{2}}

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

= 3^{3} \cdot 1283

3^{3} = 27

= 128 \cdot 273

Multiply the numbers:

128 \cdot 27 = 3456

= 34563

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Frequently Asked Questions (FAQ)

What is sqrt(12)^7 ?
The solution to sqrt(12)^7 is 3456sqrt(3)