What is 1/2 (4k^5)^2 ?

The solution to 1/2 (4k^5)^2 is 8k^{10}

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simplify 1/2 (4k^5)^2

simplify

\frac{1}{2} (4 k^{5})^{2}

8 k^{10}

Solution steps

\frac{1}{2} (4 k^{5})^{2}

Apply exponent rule:

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

(4 k^{5})^{2} = 4^{2} (k^{5})^{2}

= \frac{1}{2} \cdot 4^{2} (k^{5})^{2}

4^{2} = 16

= \frac{1}{2} \cdot 16 (k^{5})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(k^{5})^{2} = k^{5 \cdot 2}

= \frac{1}{2} \cdot 16 k^{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{1}{2} \cdot 16 k^{10}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 16 k ^{10}}{2}

Multiply the numbers:

1 \cdot 16 = 16

= \frac{16 k ^{10}}{2}

Divide the numbers:

\frac{16}{2} = 8

= 8 k^{10}

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