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Popular >

simplify (4^5)^{11/7}

Solution

simplify

(4^{5})^{\frac{11}{7}}

Solution

16384 \cdot 4^{\frac{6}{7}}

+1

Decimal Notation

53761.49789 \dots

Solution steps

(4^{5})^{\frac{11}{7}}

Apply exponent rule:

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

= 4^{5 \cdot \frac{11}{7}}

5 \cdot \frac{11}{7} = \frac{55}{7}

= 4^{\frac{55}{7}}

4^{\frac{55}{7}} = 4^{7 + \frac{6}{7}}

= 4^{7 + \frac{6}{7}}

Apply exponent rule:

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

= 4^{7} \cdot 4^{\frac{6}{7}}

4^{7} = 16384

= 16384 \cdot 4^{\frac{6}{7}}

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Frequently Asked Questions (FAQ)

What is (4^5)^{11/7} ?
The solution to (4^5)^{11/7} is 16384*4^{6/7}