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Popular >

simplify (25x^5)^{3/2}

Solution

simplify

(25 x^{5})^{\frac{3}{2}}

Solution

125 x^{\frac{15}{2}}

Solution steps

(25 x^{5})^{\frac{3}{2}}

Apply exponent rule:

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

(25 x^{5})^{\frac{3}{2}} = 2 5^{\frac{3}{2}} (x^{5})^{\frac{3}{2}}

= 2 5^{\frac{3}{2}} (x^{5})^{\frac{3}{2}}

2 5^{\frac{3}{2}} = 125

= 125 (x^{5})^{\frac{3}{2}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{5})^{\frac{3}{2}} = x^{5 \cdot \frac{3}{2}}

= 125 x^{5 \cdot \frac{3}{2}}

5 \cdot \frac{3}{2} = \frac{15}{2}

= 125 x^{\frac{15}{2}}

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Frequently Asked Questions (FAQ)

What is (25x^5)^{3/2} ?
The solution to (25x^5)^{3/2} is 125x^{15/2}