Question

√5√5√5√5√5√5 is equal to ....answer is 5 to the power 63/64 .this only i need​

Answer 1

here 2 is for square root

Answer 2

Answer:

The correct answer is $5^{\frac{63}{64}}$

Step-by-step explanation:

Step 1: If all of the following are true, a radical is said to be in simplified radical form (or simply simplified form).

There cannot be no exponents in the radicand greater than the index.

There can be no exponents in the radicand that share a factor with the index.

Under a radical, there are no fractions.

$\begin{aligned}& \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5}}}}}} \\& \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5}}}}}=\sqrt{5} \sqrt{\sqrt{5} \sqrt{\sqrt{5} \sqrt{5^{\frac{3}{4}}}}} \\& =\sqrt{5 \sqrt{5} \sqrt{\sqrt{5} \sqrt{\sqrt{5} \sqrt{5^{\frac{3}{4}}}}}}\end{aligned}$

Step 2:Apply radical rule: $\sqrt[n]{a b}=\sqrt[n]{a} \sqrt[n]{b}, \quad$ assuming $a \geq 0, b \geq 0$

$=\sqrt{5} \sqrt{\sqrt{5} \sqrt{\sqrt{5} \sqrt{\sqrt{5} \sqrt{5^{\frac{3}{4}}}}}}$

$\begin{aligned}& \sqrt{\sqrt{5} \sqrt{\sqrt{5} \sqrt{\sqrt{5} \sqrt{5^{\frac{3}{4}}}}}}=5^{\frac{31}{64}} \\& =\sqrt{5} \cdot 5^{\frac{31}{64}}\end{aligned}$

Apply radical rule: $\sqrt{a}=a^{\frac{1}{2}}=$

$\begin{aligned}& \sqrt{5}=5^{\frac{1}{2}} \\& =5^{\frac{1}{2}} \cdot 5^{\frac{31}{0^4}}\end{aligned}$

Step 3:Apply exponent rule: $a^b \cdot a^c=a^{b+c}$

$\begin{aligned}& 5^{\frac{1}{2}} \cdot 5^{\frac{31}{64}}=5^{\frac{1}{2}+\frac{31}{64}} \\& =5^{\frac{1}{2}}+\frac{31}{64}\end{aligned}$

$\begin{aligned}& \frac{1}{2}+\frac{31}{64}=\frac{63}{64} \\& =5^{\frac{63}{64}}\end{aligned}$

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