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Popular >

simplify 8^{1/4}*8^{1/4}

Solution

simplify

8^{\frac{1}{4}} \cdot 8^{\frac{1}{4}}

Solution

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

+1

Decimal Notation

2.82842 \dots

Solution steps

8^{\frac{1}{4}} \cdot 8^{\frac{1}{4}}

Apply exponent rule:

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

8^{\frac{1}{4}} \cdot 8^{\frac{1}{4}} = 8^{\frac{1}{4} + \frac{1}{4}}

= 8^{\frac{1}{4} + \frac{1}{4}}

\frac{1}{4} + \frac{1}{4} = \frac{1}{2}

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

Prime factorization of

8 : 2^{3}

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

Apply exponent rule:

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

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

= (2^{2} \cdot 2)^{\frac{1}{2}}

Apply exponent rule:

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

(2^{2} \cdot 2)^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}

= (2^{2})^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}

(2^{2})^{\frac{1}{2}} = 2

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

Apply exponent rule:

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

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

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

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

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

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

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

Apply exponent rule:

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

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

Refine

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

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Frequently Asked Questions (FAQ)

What is 8^{1/4}*8^{1/4} ?
The solution to 8^{1/4}*8^{1/4} is 2*2^{1/2}