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Popular >

simplify (5^3)^{7/6}

Solution

simplify

(5^{3})^{\frac{7}{6}}

Solution

125 \cdot 5^{\frac{1}{2}}

+1

Solution steps

(5^{3})^{\frac{7}{6}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 5^{3 \cdot \frac{7}{6}}

3 \cdot \frac{7}{6} = \frac{7}{2}

= 5^{\frac{7}{2}}

5^{\frac{7}{2}} = 5^{3 + \frac{1}{2}}

= 5^{3 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 5^{3} \cdot 5^{\frac{1}{2}}

5^{3} = 125

= 125 \cdot 5^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is (5^3)^{7/6} ?
The solution to (5^3)^{7/6} is 125*5^{1/2}