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Popular >

simplify (81m^8)^{3/2}

Solution

simplify

(81 m^{8})^{\frac{3}{2}}

Solution

729 m^{12}

Solution steps

(81 m^{8})^{\frac{3}{2}}

Apply exponent rule:

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

(81 m^{8})^{\frac{3}{2}} = 8 1^{\frac{3}{2}} (m^{8})^{\frac{3}{2}}

= 8 1^{\frac{3}{2}} (m^{8})^{\frac{3}{2}}

8 1^{\frac{3}{2}} = 729

= 729 (m^{8})^{\frac{3}{2}}

Apply exponent rule:

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

assuming

a \geq 0

(m^{8})^{\frac{3}{2}} = m^{8 \cdot \frac{3}{2}}

= 729 m^{8 \cdot \frac{3}{2}}

8 \cdot \frac{3}{2} = 12

= 729 m^{12}

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Frequently Asked Questions (FAQ)

What is (81m^8)^{3/2} ?
The solution to (81m^8)^{3/2} is 729m^{12}