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Popular >

simplify (8^{1/2})^3

Solution

simplify

(8^{\frac{1}{2}})^{3}

Solution

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

+1

Decimal Notation

22.62741 \dots

Solution steps

(8^{\frac{1}{2}})^{3}

Apply exponent rule:

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

= 8^{\frac{1}{2} \cdot 3}

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

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

Prime factorization of

8 : 2^{3}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

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

= 8 \cdot 2 \cdot 2^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 2 = 16

= 16 \cdot 2^{\frac{1}{2}}

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- 7 (1 - 4 m) = 13 (2 m - 3)

simplify 81^2 simplify

8 1^{2}

n^{2} + 2 n - 15 = 0

- (2 k - 11) = 7

Frequently Asked Questions (FAQ)

What is (8^{1/2})^3 ?
The solution to (8^{1/2})^3 is 16*2^{1/2}