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Popular >

simplify (sqrt(16))^5

Solution

simplify

(16)^{5}

Solution

1024

Solution steps

(16)^{5}

Apply exponent rule:

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

(16)^{4 + 1} = (16)^{4} 16

= (16)^{4} 16

(16)^{4} = ((16)^{2})^{2}

= ((16)^{2})^{2} 16

Apply exponent rule:

(16)^{2} = 16

= 1 6^{2} 16

Apply radical rule:

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

16 = 1 6^{\frac{1}{2}}

= 1 6^{2} \cdot 1 6^{\frac{1}{2}}

Apply exponent rule:

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

1 6^{2} \cdot 1 6^{\frac{1}{2}} = 1 6^{2 + \frac{1}{2}}

= 1 6^{2 + \frac{1}{2}}

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

= 1 6^{\frac{5}{2}}

Factor the number:

16 = 4^{2}

= (4^{2})^{\frac{5}{2}}

Apply exponent rule:

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

= 4^{2 \cdot \frac{5}{2}}

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

= 4^{5}

4^{5} = 1024

= 1024

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Frequently Asked Questions (FAQ)

What is (sqrt(16))^5 ?
The solution to (sqrt(16))^5 is 1024