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Popular >

simplify (4a^4)^{3/2}

Solution

simplify

(4 a^{4})^{\frac{3}{2}}

Solution

8 a^{6}

Solution steps

(4 a^{4})^{\frac{3}{2}}

Apply exponent rule:

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

(4 a^{4})^{\frac{3}{2}} = 4^{\frac{3}{2}} (a^{4})^{\frac{3}{2}}

= 4^{\frac{3}{2}} (a^{4})^{\frac{3}{2}}

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

= 8 (a^{4})^{\frac{3}{2}}

Apply exponent rule:

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

assuming

a \geq 0

(a^{4})^{\frac{3}{2}} = a^{4 \cdot \frac{3}{2}}

= 8 a^{4 \cdot \frac{3}{2}}

4 \cdot \frac{3}{2} = 6

= 8 a^{6}

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Frequently Asked Questions (FAQ)

What is (4a^4)^{3/2} ?
The solution to (4a^4)^{3/2} is 8a^6