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Popular >

simplify (2/5 a^4)^4

Solution

simplify

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

Solution

\frac{16 a ^{16}}{625}

Solution steps

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

Apply exponent rule:

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

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

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

(\frac{2}{5})^{4} = \frac{16}{625}

= \frac{16}{625} (a^{4})^{4}

Apply exponent rule:

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

assuming

a \geq 0

(a^{4})^{4} = a^{4 \cdot 4}

= \frac{16}{625} a^{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{16}{625} a^{16}

Multiply fractions:

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

= \frac{16 a ^{16}}{625}

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Frequently Asked Questions (FAQ)

What is (2/5 a^4)^4 ?
The solution to (2/5 a^4)^4 is (16a^{16})/(625)