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Popular >

simplify (9x^4)^{3/2}

Solution

simplify

(9 x^{4})^{\frac{3}{2}}

Solution

27 x^{6}

Solution steps

(9 x^{4})^{\frac{3}{2}}

Apply exponent rule:

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

(9 x^{4})^{\frac{3}{2}} = 9^{\frac{3}{2}} (x^{4})^{\frac{3}{2}}

= 9^{\frac{3}{2}} (x^{4})^{\frac{3}{2}}

9^{\frac{3}{2}} = 27

= 27 (x^{4})^{\frac{3}{2}}

Apply exponent rule:

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

assuming

a \geq 0

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

= 27 x^{4 \cdot \frac{3}{2}}

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

= 27 x^{6}

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Frequently Asked Questions (FAQ)

What is (9x^4)^{3/2} ?
The solution to (9x^4)^{3/2} is 27x^6