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Popular >

simplify 243^{7/10}*243^{1/10}

Solution

simplify

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}}

Solution

81

Solution steps

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}} = 24 3^{\frac{7}{10} + \frac{1}{10}}

= 24 3^{\frac{7}{10} + \frac{1}{10}}

\frac{7}{10} + \frac{1}{10} = \frac{4}{5}

= 24 3^{\frac{4}{5}}

Factor the number:

243 = 3^{5}

= (3^{5})^{\frac{4}{5}}

Apply exponent rule:

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

= 3^{5 \cdot \frac{4}{5}}

5 \cdot \frac{4}{5} = 4

= 3^{4}

3^{4} = 81

= 81

Popular Examples

3 n - 7 < 26

factor x^3-729 factor

x^{3} - 729

factor 18x^{4p+m}-66x^{2p+m}y^2-24x^my^4 factor

18 x^{4 p + m} - 66 x^{2 p + m} y^{2} - 24 x^{m} y^{4}

4/5 (x-2)< 1/3 (x-6)

\frac{4}{5} (x - 2) < \frac{1}{3} (x - 6)

3x^2-2.4x+0.41=0

3 x^{2} - 2.4 x + 0.41 = 0

Frequently Asked Questions (FAQ)

What is 243^{7/10}*243^{1/10} ?
The solution to 243^{7/10}*243^{1/10} is 81